INCOHERENT SCATTERTheory, Practice and Science

Collection of lectures given in Cargese, Corsica, 1995.

Incoherent Scatter spectra computed with a typical EISCAT observation of theionosphere in the ~ 120 - 500 km altitude range. The spectra shape varies with the

altitude as function of the observed electron temperature and of the ion temperature andcomposition. The spectral power is scaled to the electron density and the spectra are

plotted along a line shape representing the altitude profile of the electron density.

Denis Alcaydé - EditorTechnical Report 97/53 - EISCAT Scientific Association

Printed version - November 1997Electronic version – December 2001

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Table of Contents

Author's Vademecum iiEditor's Foreword iiiAcknowledgements iv

Tor HagforsPlasma Fluctuations Excited by Charged Particle Motion and theirDetection by Weak Scattering of Radio Waves

1

Wlodek KofmanPlasma Instabilities and their Observations with the IncoherentScatter Technique

33

Asko Huuskonen and Markku LehtinenModulation of Radiowaves for Sounding the Ionosphere: Theory andApplications

67

Kristian SchlegelThe Use of Incoherent Scatter Data in Ionospheric and PlasmaResearch

89

Mike LockwoodSolar Wind - Magnetosphere Coupling 121

Yoshuke KamideAurora/Substorm Studies with Incoherent-Scatter Radars 187

Arthur D. RichmondIonosphere-Thermosphere Interactions at High Latitudes 227

Jürgen RöttgerRadar Observations of the Middle and Lower Atmosphere 263

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Vademecum:Denis Alcaydé, Dr. (Editor) Denis.Alcayde@cesr.fr Centre d'Etude Spatiale des Rayonnements F-31028 Toulouse Cedex 4 - France

Tor Hagfors, Prof.: Hagfors@linmpi.mpg.de Max Planck Institut für Aeronomie - Postfach 20 D-37189 Katlenburg-Lindau - Germany

Asko Huuskonen, Dr.: Asko.Huuskonen@fmi.fi Finnish Meteorological Institute Helsinki - Finland

Yoshuke Kamide, Dr.: Kamide@stelab.nagoya-u.ac.jp Solar Terrestrial Environment Laboratory Nagoya University - Toyogawa-Aichi 442 - Japan

Wlodek Kofman, Dr.: Wlodek.Kofman@Obs.ujf-grenoble.fr Laboratoire de Planétologie de Grenoble 122 rue de la Houille Blanche - F-38041 - Grenoble - France

Markku Lehtinen, Dr.: Markku.Lehtinen@sgo.fi Sodankylä Geophysical Observatory University of Oulu - Sodankylä - Finland

Mike Lockwood, Prof.: M.Lockwood@rl.ac.uk Rutherford Appleton Laboratory Chilton-Didcot - OX11 0QX - UK

Arthur D. Richmond, Dr.: Richmond@ucar.edu High Altitude Observatory - NCAR Boulder - Colorado - 80307-3000 - USA

Jürgen Röttger, Dr.: Roettger@linmpi.mpg.de Max Planck Institut für Aeronomie - Postfach 20 D-37189 Katlenburg-Lindau - Germany

Kristian Schlegel, Prof.: Schlegel@linmpi.mpg.de Max Planck Institut für Aeronomie - Postfach 20 D-37189 Katlenburg-Lindau - Germany

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Editor's Foreword

The idea of this book came with the necessity of organising an introductoryseries of lectures for welcoming the Japanese Scientists to the EuropeanIncoherent Scatter Association. Indeed, after nearly 15 years of EISCAToperations, incoherent scatter theory, technique, practice and science havesignificantly changed, new radars have been constructed (EISCAT-ESR) andare planned for the future (the Polar Cap Radar project). Thus, in conjunctionwith the VIIth EISCAT Workshop organised in Cargese (Corsica-France) in fall1995, a series of lectures were invited and given before the Workshopholding: this book reflects most of these given lectures.

This book is intended for use by graduate students for entering the field ofIncoherent Scatter Research; it is felt however (and also hoped) that thevarious chapters of this book can be of some interest for more seniorscientists. The book organisation is such that one can find at the beginningthe main theoretical aspects of the Incoherent Scattering, followed bypractical considerations on signal modulation, echoes and data analysis, andthen scientific application aspects:

the first two chapters deal with the theoretical descriptions of scatteringof plasma waves by the ionospheric plasma; Chapter one (Tor Hagfors)describes the "classical" Incoherent Scattering, while Chapter two(Wlodek Kofman) introduces the non thermal and instabilities effects.

in Chapter three (Asko Huuskonen and Markku Lehtinen) are introducedthe basics of the modulation of the radio waves for pulsed radars. Onceionospheric echoes are received, some analysis can be made which liesupon some basic physics described in Chapter four (Kristian Schlegel).

the Solar Wind Magnetosphere interaction, Auroras and theirionospheric effects, Thermospheric Physics and the contributions made(or foreseen) by the Incoherent Scatter Observations are described inthe following three Chapters (Chapter five, Mike Lockwood; Chapter six,Yoshuke Kamide and Chapter seven, Arthur Richmond, respectively).

the final Chapter (Chapter eight, Jürgen Röttger) deals with the theory,technique and science achieved with atmospheric backscatter andreflection processes of radio waves.

The Editor has tried to keep as much uniformity as possible trough thevarious styles of the Authors. Notes in the text and references are printed initalics. The scalar symbols are in italic, the vectors are in boldface and thetensors (or matrices) are underlined and bold.

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Acknowledgements:

The Editor is happy to thank all the Authors who very hardly worked forproducing a written version of their Cargese lecture; all Authors have kindlyprovided the Editor with almost all the necessary materials (texts, equationsand figures) close to their final form, thus making the Editor work muchsimplified.

The Editor would like also to deeply acknowledge the Director of EISCAT, Dr.Jürgen Röttger, who have accepted to use the "EISCAT-Technical Reports"series as the practical printing, publishing and distribution of the book.Thanks are also given to several colleagues who have, in the CESR, "peu ouprou" contributed to the final edition of the book, and finally to Anette Snallfotin EISCAT-HQ who has so kindly helped and served as the intermediatebetween the Publisher and the Editor.

This Editor's work has been made possible through partial funding of the GdRPlasmae of CNRS.

EISCAT is an international association, supported the research councils ofFinland, France, Germany, Japan, Norway, Sweden and the United Kingdom.

Denis Alcaydé - November 1997

Electronic version – December 2001

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1

PLASMA FLUCTUATIONS EXCITED BY CHARGED PARTICLEMOTION AND THEIR DETECTION BY WEAK SCATTERING OF

RADIO WAVES

Tor Hagfors

1. IntroductionIf spatial fluctuations or variations in refractive index exist in a medium a wave

cannot propagate through it unperturbed because energy will be scattered by the re-fractive index variations into other directions. In most cases the spatial fluctuationsare also time dependent, and the time variation of the scattered wave will no longerbe the same as that of the unperturbed wave. Such phenomena have been studied inmany branches of physics, notably in connection with tropospheric and ionosphericscattering of radio waves by irregularities caused by turbulence. In the latter case thedensity fluctuations are caused through the action of external macroscopic sources.The fluctuations that we are about to discuss in the present paper are caused by thefact that the plasma is built of discreet charged particles. When these particles aremoving through the plasma they will excite electron density fluctuations which canbe detected by electromagnetic wave scattering. This is the type of scattering whichhas become known as "incoherent scattering".

There is available a large number of papers dealing with the theory of incoherentscattering of radio waves, particularly with reference to the ionosphere. [Gordon,1958; Fejer, 1960; Dougherty and Farley, 1960; Salpeter, 1960; Renau 1960; Hag-fors, 1961; Rosenbluth and Rostoker, 1962]. Later important additional contributionshave been made by Woodman [1965], Moorcroft [1964] and Perkins et al. [1965].Rather complete discussions of the subject matter have been given by Sitenko [1967]and by Sheffield [1975].

The observations made over the last decades have shown that incoherent scatter-ing has become one of the most fruitful methods of investigating the ionosphere toheights of several thousand kilometres from the ground. [Bowles, 1958; Pineo et al.,1960; Millman et al., 1961; Bowles et al., 1962]. Excellent reviews of the experi-mental work have been given by Evans [1968] and Beynon and Williams [1978]

The method is particularly useful because in addition to providing data onelectron density it is also capable of giving information on parameters such aselectron and ion temperatures, the ionic composition, or the orientation of themagnetic field. The extension of routine measurements to include the region abovethe peak of the ionosphere is of great importance to the understanding of

2

the behaviour of the ionospheric layers. It is interesting that incoherent scattering hasalso found application as a diagnostic tool for hot plasmas in thermonuclear researchfollowing the development of practical laser sources. [Rosenbluth and Rostoker,1962].

The first suggestion that incoherent scattering might be used to measure electrondensity in the ionosphere was made by Gordon [1958]. Gordon estimated the totalscattered power by adding powers scattered by individual electrons and concludedthat present day radars had sufficient sensitivity. He also inferred that the wavesscattered by the plasma would be subject to Doppler broadening, and predicted theamount of broadening by adding power scattered by individual electrons travellingwith velocities corresponding to a Maxwellian velocity distribution. The first obser-vations by Bowles [1958] showed that the predicted spectral broadening in particularwas seriously in error.

Subsequent theoretical work explained the discrepancy as due to neglect of parti-cle interactions in the original theory. It was shown that the width of the broadenedlines should correspond with the thermal speed of the ions rather than that of theelectrons. The total power scattered was shown to be less than predicted by Gordonby a factor of 1/2 in most cases of interest provided ions and electrons are at thesame temperature. For hot electrons and cold ions - a situation which often prevailsin the ionosphere - the power is often less than this [Buneman, 1962].

When an external magnetic field is included in the considerations additional com-plications arise. Bowles [1961] suggested that spectral distributions might containlines corresponding to ionic gyro resonances. This suggestion has been confirmedtheoretically, and the conditions have been given under which ion lines might be ob-served, [Salpeter, 1961; Hagfors, 1961; Farley et al., 1961; Fejer, 1961].

It appears that the theoretical analysis - i.e. the first order analysis - is more or lesscomplete in that several workers have arrived at identical or nearly identical conclu-sions based on widely different approaches. In all results, however, with the excep-tion of that of Farleyet al. [1961], the excitation of hydromagnetic waves by the mi-croscopic motions is missing. Discussions of the interaction with transverse modeshave also been given by Sitenko [1967] and by Sheffield [1975]. In most calculationsof fluctuations only Coulomb interactions are accounted for and this seems to beadequate for ionospheric purposes.

In the present paper an attempt is made to rederive the expressions for thescattering from first principles and fairly readily understandable pictures. Thisbecomes particularly simple when we make full use of the concept of "dressedparticles" first introduced into plasma physics by Rosenbluth and Rostoker

3

[1962]. The gain in physical insight using the dressed particle concept is purchasedat the cost of some rigor.

Section 2 deals with the problem of evaluating the total scattered power and thespectral distribution of this power in terms of the properties of the plasma. A generaldiscussion is then given in Section 3 of the various factors determining these proper-ties of the plasma, beginning with a plasma of noninteracting particles, with or with-out an external magnetic field, proceeding with the effect of paricle interaction in theform of collective electrostatic interaction, and ending up with power spectra of thefluctuations under various physical conditions.

2. The Relationship of Scattering to Electron Density Fluctua-tions

We first compute the power reradiated by a certain volume V of a plasma which isirradiated by a plane monochromatic wave with wave vector at a frequency ωmuch higher than the plasma frequency for electrons ωpe defined by:

ωpe =

n0 qe

2

m ε0

1/2(1)

where:

n0 = electron densityqe = electron chargem = mass of an electronε0 = dielectric constant of free space.

Rationalized MKSA units will be adhered to throughout.

The field scattered by a single electron within the volume V, see Figure 1, willthen be:

Ep = Ein exp i (ω0 t - .rp(t) 1R0

exp-i ω0

c R0 σ0 exp i K.rp (t) (2)

Here r(t) is the position of the particle at time t and σ0 is the effective scattering "ra-dius" of the electron defined by:

σ0 = r0 sinχ =

qe2

4π ε0

1m c2 sinχ (3)

4

Figure 1. Scattering from electron at position rp(t).

where χ is the angle between the electric field vector of the incident wave and K, i.e.the direction toward the observer. Certain complications might arise through thepresence of an external magnetic field, but these will not be considered here.

We see that the scattering is determined by the difference of the wave vectors of

the incident and the scattered waves, k = - K. On the assumptions of weak scat-tering the total field at the observer becomes:

Eobs = Ein σ0

R0 exp

i (ω0 t - ω0

c ) R0 ∑p

exp -i k.rp (t) (4)

where the summation is extended over all the electrons within the volume V.

It will prove convenient to express the scattered field in terms of electron densityn(r,t). Because electrons are here considered as point particles the number density ismost easily expressed as a sum of δ-functions in space:

n(r,t) = ∑p

δ r - rp (t) (5)

We now expand in spatial Fourier series within a periodicity cube of volume V:

5

n(r,t) = ∑k

n (k,t) . e i k.r (6a)

with:

n (k,t) = 1V

⌡⌠

d(r) n(r,t) e i k.r (6b)

The observed field Eobs can therefore be expressed as:

Eobs = σ0

R0 Ein . V . n(k,t) exp -i ( ω0 t -

ω0

c R0 ) (7)

It follows from this result that the signal observed at the receiver with a planemonochromatic wave incident on the volume V has the character of a modulated sig-nal centred on the carrier frequency ω0 [approximately !] and with complex ampli-tude proportional to n(k,t), k being the wave vector difference as introduced above.The complex amplitude hence becomes:

Aobs (t) = σ0

R0 Ein v . n(k,t) (8)

The statistical properties of the complex amplitude at the receiver are therefore thesame as those of n(k,t). The received signal is conveniently described statistically bythe autocovariance:

⟨ A*(t) A(t + τ) ⟩av (9)

and the power spectrum is found by Wiener - Khinchine’s theorem as the Fouriertransform of this:

Pobs (ω) = σ02

R02 Ein2 . N . φ (k,ω) = N . PT .φ (k,ω) (10)

where PT is the total power scattered by a single electron under the same geometrical

conditions, N is the total number of electrons in the volume V and φ (k,ω) is the Fou-rier transform of the autocorrelation function of electron density fluctuations:

ρ(k,τ) = V2

N ⟨ n*(k,t) n(k,t + τ) ⟩av (11)

6

Figure 2. Geometry of incident and scattered waves.

Note that the omission of the exponential time variation expi ω0 t has shifted the

power spectrum of the received signal Pobs(ω) down to zero frequency. The fre-

quency ω from now on only corresponds to the amount of Doppler displacementfrom the transmitted frequency ω0.

Physically we may visualize the scattering to occur as follows: at any given timethere is present in the scattering volume electron density waves travelling in all dif-ferent directions with all different wavelengths. The transmitter-receiver geometryrepresented by the wave vectors and k picks out one particular of these "waves" asresponsible for the scattering. With a scattering angle ϕ, see Figure 2, the wavelengthof these density waves is:

Λdens = λ

2 sin (ϕ / 2) (12)

where λ is the radio wavelength. The strong resemblance of this formula with thecondition for reflection in a crystal lattice given by Bragg should be observed [Fig-ure 2].

Doppler shift ω now corresponds to motion of our particular density variation. Foreach velocity there is a corresponding Doppler frequency ω . The velocity v, positivealong positive k, is related to the Doppler shift frequency ω through:

v = λdens . ω

2π = - ω . λ

4π sin (ϕ / 2) = -

ω|k| (13)

7

With this discussion the whole problem of the scattering process has been tied toproperties of the plasma and density fluctuations therein. Such fluctuations are stud-ied in detail in the following sections.

3. Electron Density FluctuationsIn the discussions to follow we neglect the effect of binary collisions on the den-

sity fluctuations. This is a good approximation in a sufficiently dilute plasma such asthe upper part of the ionosphere, where collective interactions tend to dominate. Inthe first of the subsections to follow we also neglect long range interactions, andconsequently begin our considerations with a gas of non-interacting particles. Such agas will lack many of the familiar properties of gases - for instance it will be unableto support ordinary sound waves. A discussion of such a peculiar plasma is never-theless useful; because, as will be shown later on, a plasma with particles interactingthrough electromagnetic fields will in first order behave as if the particles move in-dependently, but with a cloud of charge surrounding them - as if "dressed".

The random thermal motion of individual particles will represent charge and cur-rent fluctuations due simply to the discreetness of the particles. This is a sort of "in-trinsic fluctuation" associated with the atomicity of the gas. When in the second sub-section we go on to consider electromagnetic field interactions it will be shown thatthe interaction fields can be regarded as excited by the charge and current fluctua-tions caused by the thermal motion of individual particles. These fields in turn willinduce fluctuations in the plasma, and these "induced fluctuations" are superimposedon the intrinsic fluctuations caused directly by the discreet nature of the particles.The discussion will allow non-equilibrium situations to prevail, although the distri-butions must be stationary in the Vlasov sense. Most formulae actually given explic-itly will apply to a quasiequilibrium situation where electrons and ions are separatelyin equilibrium but not necessarily at the same temperature. Whenever explicit calcu-lations are carried out the velocity distributions will be taken as Maxwellian.

3.1. Fluctuations in a Gas of Non-Interacting ParticlesWe consider the motion of charged particles in rotating coordinates defined as

follows:

Cartesian: Rotating:

r = x,y,z r1 = 12

(x + i y)

r-1 = 12

(x - i y)

r0 = z

(14)

8

Here the z-axis which is the axis of symmetry coincides with the direction of theexternal magnetic field B0. From Eq. 14 it is obvious that there is a unitary transfor-mation between Cartesian and rotating coordinate systems. For the equation of mo-tion of a single particle we obtain:

v.α = - i

q B0

m α va = - i α Ω va (α = 1, -1, 0) (15)

For the time being we allow the gyrofrequency Ω to be negative for electrons andpositive for ions. This brings out the real advantage in using rotating coordinates: theequations of motion are diagonalized.

If at the present time t the velocity and position of the particle are v (t) = v+1;v-

1;v0 and r (t) = r+1;r-1;r0 then the particle velocity and position at an earlier timet’ must have been:

vα (t') = vα (t - τ) = vα (t) . ei α Ω t (16a)

Or in vector form:

v(t - τ) = Γ.(τ) v(t) (16b)

where Γ.(τ) is a matrix transforming from present to past velocities. In polarised co-

ordinates the matrix is on diagonal form. Similarly past and present particle positionsare related through:

rα(t - τ) = rα(t) - ei α Ω t - 1

i α Ω vα(t) (17a)

or again in vector form:

r(t - τ) = r(t) - Γ(τ) v(t) (17b)

Γ (τ) transforming from present to past position is also on diagonal form in ourcoordinate system. The elements of the matrices describing the screw motion of theparticles are:

Γ.αα = g

.α = ei α Ω t (18)

and

Γαα = gαα = ei α Ω t - 1

i α Ω (19)

9

In Section 2 we saw that each particle contributes an amount

np (k,t) = 1V e-i k.rp(t) (20)

to the Fourier transform of the particle density giving rise to the scattering. The com-plex autocorrelation in particle density associated with a single particle becomes:

⟨ np*( k, t) np( k, t+τ)⟩av = ⟨ np*( k, t-τ) np ( k, t)⟩av =

1V2 ⟨ e(-i k-α gα vα )⟩av = (21)

1V2

⌡⌠

d(v) fo(v) e -i a.v

Here f0(v) is the velocity distribution of the particles and a is a vector defined by:

a-α = k-α gα = k-α e i Ω α τ -1

i Ω α (22)

The complex autocorrelation function normalized as in Eq. 11 becomes:

ρ (k,τ) = ⟨ e -i a.v ⟩av (23)

The correlation function for density fluctuations in a gas of non-interacting parti-cles is therefore a function of the vector a and of the parameters of the single particlevelocity distribution.

The Fourier component of single particle current density similarly becomes:

jp (t) =qV vp (t) e-i k.rp(t) (24)

A statistical description of this random current is provided by the autocovarianceof the rotating components of the current:

⟨ jµ* ( k, t) jν* ( k, t+τ)⟩av = ⟨ jµ* ( k, t-τ) jν* ( k, t)⟩av=

q2

V2 g.-µ

- ∂ 2

∂ aµ ∂ aν ρ (k,τ) (25)

Because of the independency of the particles the expression for the total current isobtained by multiplication by N, the total number of particles.

10

The normalized autocorrelation function ρ (k,τ) thus enters both in the determina-tion of current and charge density fluctuations. Before giving a specific form forf0(v) and hence for ρ (k,τ) it is worthwhile to discuss in a rather qualitative mannersome of the properties of this function, or its Fourier transform which is the powerspectrum.

As was explained in Section 2 the density fluctuations can be thought of as a su-perposition of density waves travelling in all different directions with all differentvelocities and wavelengths. Suppose first the k is along the magnetic field. The par-ticle motion in this direction is independent of the field and we expect the densityfluctuations to be the same as if no magnetic field were present.

The density waves are carried along k by beams of particles with thermal veloci-ties equal to the wave velocities, and with amplitudes proportional to the number ofparticles in the beams. Because the number of particles in each beam specified by thevelocity v = ω/k is proportional to f0(v//) the power spectrum in this case is just pro-portional to the velocity distribution along the magnetic field with v// replaced by

(ω/k). The autocorrelation ρ (k,τ) is the Fourier transform of this power spectrum.

Figure 3. Typical particle trajectory shown in relation to a density wave . Transverse case, β = 90°,large Larmor radius.

11

At the other extreme, that of k perpendicular to B0 the density waves are travellingat right angles to the field. In Figure 3 the magnetic field is along the z-axis and thewaves are travelling in the x-direction. Furthermore the radius of gyration, or theLarmor radius defined by:

R = 2 vth

Ω (26)

[where vth is the r.m.s. thermal velocity] is large compared with the density wave-length. Suppose the particle density projected into the x-y plane at t = 0 is of theform shown to the extreme left. Redistribution of particles along the x = constantplane will have no influence on the density component under consideration. If wepick out any straight line parallel to the magnetic field characterized by x0y0 the par-ticles leaving this line with any velocity in any direction will return to this line afterexactly one period of gyration T = 2π/Ω. The density will therefore be a repetitivetime function with period T, and this periodicity must also appear in the autocorrela-tion function.

In the example shown in Figure 3 the radius of gyration of a thermal particle islarge compared with the wavelength of the density waves and the particles can travelalong with the density wave at least for a few wavelengths before being bent awayfrom the direction of the wave. Had we chosen the radius small compared with thewavelength of the density variation, the time variation would lose the character of awave phenomen because the particles would be so strongly attached to the magneticfield lines that they would no longer be able to transport a spatial variation along kby even as little as one wavelength.

The spatial variation would then tend to appear as a nearly stationary pattern, andthe power spectrum would be extremely [Figure 3] narrow. In the autocorrelationpicture a small Larmor radius, i.e. a strong magnetic field, would give an autocorre-lation function close to unity for all time shifts τ. The periodic modulation of ρ (k,τ)so prominent for large Larmor radii would be rather shallow in this case.In scatteringof radio waves from the ionosphere at frequencies less than about 1000 MHz theLarmor radius of electrons will be small and that of the ions large compared with thedensity scale of interest, i.e. Λdens = λ / 2 sin(ϕ / 2).

As we have just seen there is no effect of a magnetic field in the longitudinal case[β = 0°] but there is a profound effect for the transverse case [β = 90°]. Let us nowexamine what happens in the intermediate range. We start by letting decrease βslightly from 90°.

As long as β is exactly 90° motion of the particles along the magnetic field doesnot matter because this only corresponds to motion along planes of constant

12

phase of the density waves. As soon as the perpendicularity condition is relaxed,motion along the field does indeed matter, because when the particle gyrates onceround the field line that it left T seconds earlier, it might at the same time have slidalong the field line to such an extent that it no longer fits into the original phase re-lationship with the density wave. In the case of large Larmor radius the condition forspectral lines to occur in the power spectrum can be found by considering Figure 4.

The projection is here shown of a typical particle trajectory into a plane containingthe magnetic field B0 and the propagation vector k. The typical velocity along themagnetic field is vth where vth is the thermal velocity in the z-direction. The typicaldistance of motion of this particle along the magnetic field during one period of gy-ration becomes:

1 = vth .T = vth . 2πΩ = 2 R .

2 . vth

Ω = 2 π . R (27)

where R is again the Larmor radius as defined in Eq. 26. The motion of the particlealong the wave normal k during the same time becomes:

∆ s = 1 . cos β = 2 π R cos β = 2 π R sin ψ (28)

Now, if the motion of the particle along the field line during one period of gyra-tion has caused the particle to get out of step, or out of phase with the density varia-tion, then the deep periodic modulation of the autocorrelation function will disap-pear. For large Larmor radii the condition for the magnetic field to have an apprecia-ble influence on the spectrum becomes:

Figure 4. Particle trajectory in relation to a density wave for arbitrary β.

13

k . ∆ s < π2 or: sin ψ <

12 2 k R

(29)

which is the condition for the particle to keep in phase with the density variation forat least one period of gyration.

For small Larmor radii the modulation of the spectrum is never very prominent. Inpassing from β = 90° to β = 0° the autocorrelation function will just gradually shrinkfrom being close to unity for all τ at β = 90° to the no-magnetic field case at β = 0°.The spectrum will therefore be narrow when β = 90° and identical with the no-magnetic field case at β = 0° with a gradual transition between the two cases. This iseasily understood by considering the particles as completely constrained to movealong the field lines. The r.m.s. motion along the direction of k - and this is the com-ponent of motion giving rise to the spectral broadening - is then simply:

vk = vth . sin ψ (30)

and the width of the power spectrum is just proportional to vth2 sin2 ψ = vth2 cos2 β.

In order to check the rather intuitive conclusions regarding the properties ofρ (k,τ) this function was evaluated for a Maxwellian velocity distribution:

f0 (v) =

2π

vth2

3/2

e-v2/2vth2 (31)

where vth is the r.m.s. thermal velocity defined by:

vth2 = θ / m θ being the absolute temperature, in energy units.

The result is:

ρ (k,τ) = e -½ vth2 |a|2=e-(kR)2 ( ½Ωτ)2 cos2β + sin2(½Ωτp) sin2β (32)

This result is plotted on a log-linear diagram in Figure 5, correlation against nor-malized time shift Ωτ/2π = τ/T [T = time of gyration] with the angle β as parameter.It will be seen from Figure 5 that the autocorrelation function exhibits exactly theproperties arrived at by the more qualitative arguments just presented. Modulation isonly prominent when β is close to 90° and Larmor radius large, depth of modulationdecrease with Larmor radius.

The integral over the spectrum Φ (k,ω) over all frequencies f, which is propor-tional to the total scattered power, is equal to ρ (k,ω). This is unity in all cases

14

considered so far. Independent particles therefore scatter incoherently, i.e. the scat-tered power is obtained by adding powers scattered by individual particles. The ef-fect of magnetic field is to redistribute the power whilst all the time keeping the totalscattered power constant.

The actual spectral function Φ (k,ω) becomes:

Φ (k,ω) = Re

⌡⌠

-∞

∞ ρ(k,τ) e- iωτ dτ (33)

because ρ (k,τ) will be assumed to be real and symmetric in τ. When steady drifts aresuperimposed this is no longer the case and the spectrum must be obtained with somecare. For the Maxwellian velocity distribution the spectrum becomes:

Φ(k,ω) = 2 ⌡⌠

0

∞ e-½ vth

2 |a|2 cos ωτ dτ (34)

Figure 5. Autocorrelation of independent particle number density [logarithmic scale] versus nor-malized time shift [ωτ/2π] with angle β as parameter.

15

For later purposes we define the function

G(k,ω) = ⌡⌠

0

∞ e-½ vth

2 |a|2- iωτ dτ (35)

and term it a Gordeyev integral. In terms of this function the spectrum may be ex-pressed as:

Φ(k,ω) = 2 Re G(k,ω) (36)

3.2. The Effect of a Random Electric FieldWith electromagnetic particle interaction present the motion of individual particles

becomes more complicated because each particle moves in the field of all the others.In this subsection we want to determine the density variations induced by the inter-action field. Such density variations come in addition to the density fluctuationscaused by the discreetness of the particles, i.e. the intrinsic fluctuation dealt withabove. The induced fluctuations may be computed as if the particles were smearedout into a continuum. The fields giving rise to these induced fluctuations must, how-ever, be computed from the discreet particle picture of the non-interacting gas. Fromthis we realize that there are two contributions to the density fluctuations, one fromthe discreetness of the particles, the intrinsic part, and another one due to fluctuationsinduced by the fields - which in turn are caused by the discreetness of the chargedparticles. A charged particle moving through the plasma in itself constitutes a fluc-tuation, but in addition it induces a fluctuation in the surrounding medium due to thefields it sets up. The particle plus the charge cloud surrounding it is often referred toas a "dressed particle" [Rosenbluth and Rostoker, 1962].

Assume first that the force per unit mass is known throughout the plasma, and letthis force be denoted by F(r,t). The density fluctuation induced by this force in avolume element having velocity v at position r at time t is then found from the Vla-sov equation to be:

δ n (r,v,t) = - n0 ⌡⌠

-∞

t F(r’,t’) .

∂ f0 (v’)

∂v’ dt’ (37)

The integration is extended over the orbit of the volume element at all earliertimes. If the unperturbed velocity distribution f0(v) is isotropic the force F(r,t) can beexpressed as q E(r,t) where E is the internal electric field caused by the

16

discreetness of the particles. The magnetic force vanishes because under the isotropyassumption this force is perpendicular to [∂ f0 / ∂ v]. The presence of externally ap-plied fields can always be accounted for in the computation of individual particleorbits. With a Maxwellian velocity distribution we obtain:

δ n(r,v,t) = n0 q

mvth2 ⌡⌠

∞

t E(r’,t’) . v’ f0(v’) dt’ (38)

Physically this corresponds to the energy acquired by the volume element arrivingat r at time t with velocity v from the electric field divided by the mean energy of athermal particle. The integration is along actual particle orbits. If the fluctuating fieldis rather small the perturbation in particle orbits due to the random field will besmall, and the integration can be carried along orbits which are unperturbed by therandom field. Relations between past and present velocities and positions are there-fore the same as in a gas of noninteracting particles as studied in the previous sec-tion.

In this study we are interested in spatial fluctuations irrespective of the velocity ofarrival v and we therefore average over all velocities of arrival making use of the factthat f0(v) = f0(v’) for unperturbed orbits, and obtain:

δ n(r,t) = n0 q

mvth2 ⌡⌠

d(v) f0(v)

⌡⌠

-∞

t E(r’,t’) dt’ (39)

We next expand the electric field E(r’,t’) in a spatial Fourier series:

E(r’,t’) = ∑k

E(k,t’) e ik.r’ (40)

Putting t’ = t - τ and making use of the relations between past and present posi-tions derived in Section 3.1 we obtain:

δ n(r,t) = n0 q

mvth2 ∑k

e ik.r

⌡⌠

0

∞ dτ E(k,t-τ)

⌡⌠

d(v) f0(v) Γ

.(τ) v e-ikΓ(t)v (41)

17

It follows that the spatial Fourier components of the field induced fluctuation be-come:

n1 (k,t) = n0 q

mvth2 ⌡⌠

0

∞ dτ T(k,τ) . E(k,t-τ) (42)

where we have introduced a vector T(k,τ) with rotating components:

Ta (k,τ) = ⌡⌠

d(v) f0(v) g

.a(τ) va e-ia.v = g

.a(τ)

i ∂

∂ a-a ρ(k,τ) (43)

where a is again the vector defined in Eq. 22, and where ρ(k,τ) is the autocorrelationfunction of density fluctuations of non-interacting particles.

Equation 42 should be compared with the equation relating the current density andthe electric field in a dispersive medium:

j (k,t) = ⌡⌠

0

∞ dτ σ(k,τ) E(k,t-τ) (44)

where σ(k,τ) is the conductivity tensor of the medium. We might say that σ(k,τ) de-scribes the way in which the medium responds with a current to an applied electricfield. In the same way we might interpret the vector (n0 q)/(mvth2) T(k,τ) as describ-ing the way in which the medium responds with a density variation to an appliedelectric field.

The superscript "1" will henceforth be used to signify the field-induced fluctuationas distinguished from the intrinsic fluctuation which henceforth will be labelled bysuperscript "0". The total fluctuation in the plasma now becomes:

n(k,t) = n0 (k,t) + n1 (k,t) (45)

As the field E and the response vector T appear as a one-sided convolution inte-gral it will be more convenient to work in the frequency domain. In this way we de-termine power spectra directly without going via the autocorrelation function whichproved so convenient in the description of a gas of non-interacting particles. For theinduced fluctuation we obtain:

n1 (k,ω) = E(k,ω) T(k,ω)

n0 q

mvth2 (46)

18

We must be careful in defining T(k,ω) - it is a one-sided Fourier transform:

T(k,ω) = ⌡⌠

0

∞ T(k,τ) e-iωτ dτ (47)

This is due to the one-sided convolusion which in turn is caused by the fact that onlythe past not the future can determine the fluctuation at the present time.

The field E(k,ω) is a superposition of the fields from the individual particles of theplasma. If we compute the field from one particular particle we will be able to deter-mine the fluctuation induced by this particle alone. Let this induced one-particlefluctuation be denoted by np1(k,ω). Suppose we are interested in electron densityfluctuations. The contribution to these from a particular electron p becomes:

np (k,ω) = np0 (k,ω) +

n0 q

mvth2 Epe (k,ω).Te (k,ω) (48)

where np0 (k,ω) is the intrinsic fluctuation associated with electron p. In the second

term which represents induced fluctuation, the electric field Epe (k,ω) is that associ-ated with particle p only. The intrinsic term may thus be associated with the "bare"particle and the second term with the "dressing" surrounding the particle - on the av-erage an electron repels other electrons thus creating an electron deficiency in itsneighbourhood. In addition to the "electron dressing"the electron will also be ac-companied by an "ion dressing" due to the average attraction of ions by the electron.

For a Maxwellian velocity distribution the components of T(k,ω) can be deter-mined by means of Gordeyev integrals:

Ta (k,ω) = - vth2 . ka G(k,ω - αΩ) - G(k,ω)

α Ω (49)

For α = 0 or when ω → 0 we must take the limit of this which does not exist. Forα = 0 we have:

T0 (k,ω) = vth2 . k0 . ∂ G(k,ω)

∂ ω (50)

19

We see that, when ω → 0 the vector T(k,ω) becomes parallel to the vector k. Thismeans that the only component of the electric field which can induce fluctuations isthat along k, i.e. EL defined by:

EL = 1k2 k (k .E) (51)

As this component of the field is determined by the charge fluctuations alone itmeans that the Coulomb interaction approximation is no approximation at all but anexact solution of the first order fluctuation problem in this particular case.

An ion can of course only contribute to electron density fluctuations through aninduced fluctuation, or, if we like, through its electron "dressing". The electron den-sity fluctuation associated with an ion p is therefore:

np(k,ω) = n0 qe

mvth2 Epi (k,ω) . Te (k,ω) (52)

where Epi (k,ω) is the field induced by the particular ion p.

Once these elementary contributions have been determined the total electron den-sity fluctuation can be found as a superposition of contributions from all the "dressedelectrons" plus all the ion "dressings":

⟨|n(k,ω)|2⟩av = contribution from "dressed electrons"+ contribution from ion "dressings".

Before further progress can be made we must calculate the electric field set up inthe plasma as a result of the motion of a charged particle along an unperturbed orbit.As most calculations of this electric field in connection with plasma fluctuations tac-itly assume the longitudinal interaction [= Coulomb interaction] to be the only formof interaction,we shall devote the next subsection to the calculation of this field.

3.3. The Effective Field of a Charged Particle Moving Through thePlasma

The inducing electric field Ep(k,ω) associated with the motion of a charged parti-cle may be calculated by solving Maxwell’s equations in vacuo by a Fourier trans-form in space and time assuming the field to be excited by a current jp(k,ω) which

consists of two terms, one is the driving or intrinsic term jp0(k,ω) caused directly bythe motion of the discreet particle - this is identical with the current studied in Sec-tion 3.1 - and the other term is an induced current caused by the field set up.

20

We now imagine the field Ep(k,ω) to be split in a longitudinal part EL [see Eq. 51]

and a transverse part ET (k,ω) defined as:

ET (k,ω) = - 1k2 (k x (k x E)) (53)

Here we shall consider only the longitudinal interaction. This is exactly correctwhen there is no magnetic field so that the transverse and the longitudinal modes de-couple exactly. When there is a magnetic field present there is a coupling, but thetransverse field in general only becomes important for such small values of k that itis of no interest in scattering from the ionosphere. We obtain:

n1p(k,ω) = n0 qe

mvth2 ET . T = n0 qe

k2mvth2 [ k.Ep(k,ω) ] [ k.T0(k,ω)] (54)

and the scalar product k.Ep (k,ω) can be related directly to the charge density fluc-tuation associated with the motion of a particle p. If this particle is an electron, thecharge density fluctuation becomes:

ρpe (k,ω) = qe n0p (k,ω) + n1p (k,ω) + qi N1p (k,ω) (55)

The last term qi N1p (k,ω) is the fluctuation induced by the electron p in the iondensity. When several ionic constituents are present it must be summed over similarterms, one for each constituent. For simplicity we only assume one type of positiveions to be present, and that these have mass M, thermal velocity Vth and average den-sity N0 sufficient for neutrality of the plasma as a whole. Introducing Debye lengthsfor electrons and ions we have:

De2 = ε0 mvth2/n0 qe2 = (vth/ωpe)2

Di2 = ε0 MVth2/N0 qi2 = (Vth/ωpi)2 (electrons)

(ions) (56)

where ωpe and ωpi are the plasma frequencies for electrons and ions respectively.The Debye length is therefore the distance travelled by a thermal particle during oneperiod of a plasma oscillation. Combination of these quantities with Eq. 54, 56 andwith the equation

k.Ep (k,ω) = - ρpc (k,ω) (57)

which follows from Maxwell’s equations, gives for the longitudinal field:

ELp (k,ω) = - i k . (qe/ε0k2) n0pe (k,ω)

1 + i (1/kDe)2 k.Te + (1/kDi)2 k.Ti(58)

21

When the field-inducing particle is an ion we only have to replace qen0pe(k,ω) by

the similar expression for an ion, viz. qiN0pL(k,ω). Replacing the expression

i (1/kD)2 k.T by the more commonly used longitudinal susceptibility χ = kχt k/k2, wesee that the denominator in Eq. 58 enters as a dielectric constant of the plasma, andthe field set up is a screened field.

From these considerations we can write down directly the total fluctuation associ-ated with a single electron:

npe (k,ω) = (1 + χi) n0pe(k,ω)

1 + χi + χe (59)

and for the electron density fluctuation induced by a single ion [assuming qe = - qi

!]:

npe (k,ω) = = χe N0pi(k,ω)

1 + χi + χe (60)

The total fluctuation of electron density is obtained as a superposition of fluctua-tions from all the individual particles - now being regarded as independent. This pro-cedure, which has been termed by Rosenbluth and Rostoker [1962] a "superpositionof dressed test particles" gives the correct first order fluctuation for Coulomb inter-action only. By inverting the above expression for electron-density fluctuation fromk,ω space into r,t space we could study in detail the electron cloud associated withthe motion of an ion. Fast ion motion would give a wake of electron density distur-bance travelling away from the inducing ion. The above expression therefore repre-sents the kinetic theory result of the problem of a charged particle passing through aplasma. It should be observed that the above expressions are valid for Coulomb in-teraction only.

3.4. Spectral Distribution of FluctuationsFrom Eq. 59 and 60 we can now construct the spectral distributions by simple su-

perposition of independent dressed particles. For electrons and one kind of positiveions we obtain:

⟨| ne (k,ω) |2 ⟩av = |1 + χi|2 ⟨|n0e (k,ω)|2⟩ + |χe|2 ⟨|N0i (k,ω)|2 ⟩

| 1 + χe +χi |2 (61)

where ⟨|n0e (k,ω)|2⟩ and ⟨|N0i (k,ω)|2⟩ are the power spectra of independent electronsand independent ions as studied in Section 3.1.

22

Figure 6. Characteristics of the equilibrium spectra for various Debye lengths, expressed in termsof Xp=1/kD

This result is identical with results derived by other workers. In our derivation ofEq. 61 we did make use of Maxwellian velocity distributions for ions and electronsto define vth. We are, however, perfectly free to prescribe a non-equilibrium situationwith electrons and ions at different temperatures. Also, with many different types ofions present we only have to replace the ion terms above by a sum of such ion termssubject only to neutrality of the plasma as a whole. This has been carried out byBuneman [1961] in detail. We also observe that by starting with a non-Maxwellianvelocity distribution we can work through exactly the same steps as above and endup with distributions for relative drifts of electrons and ions or other non-equilibriumsituations we might like to examine. The procedure of superposing dressed particlesis therefore a very flexible one. Figure 6 shows power spectra for equilibrium condi-tions as kD=1/Zp changes.

Here we shall retain the Maxwellian distributions of velocity - but allow electronsand ions to be at different temperatures. Figure 7 shows the ion line spectra for vari-ous values of θe/θi. For small wavelengths of the density fluctuations, when kD → ∞we see that the electron density fluctuations become identical with the no-interactioncase. - Over distances less than the Debye length the charged particles then move asif completely free. - As the wavelength of the fluctuation increases, the ions are ableto induce a fluctuation in the electron density at the scale of the wavelength.

23

Figure 7. Ion line fluctuation spectra for varying temperature ratios θe/θi

At frequencies ω less than about kVth, Vth being the ionic thermal velocity, theterm kTe is roughly equal to i, or of order unity. Within the same frequency range theterm kTi is at most of order unity. At the same time the unperturbed electronic spec-tral density is of order 1/kvth and that for the ions of order 1/kVth . The order of mag-nitude of the terms induced by the ions and from dressed electrons in the nominatorbecomes:

electronic termionic term

(1/θi)2 . 1/vth

(1/θe)2 . 1/Vth ∼

θe

θi

3/2

m

M

1/2(62)

Note that here θe and θi are electron and ion temperatures respectively. As long asthe temperatures are of the same order of magnitude the electronic term is unimpor-tant because (m/M)1/2 ≤ 1/43. At moderate temperature ratios the electron densityfluctuations are mainly caused by fluctuations induced by ions, as long as ω < kVth

and kD < 1. The main features of the spectrum at low frequencies

24

must exhibit many of the same characteristics as the ion spectrum. In particular thecondition for lines to occur in the electronic spectrum must be determined as in ourdiscussion of Section 3.1 with ion parameters. The shape of the spectrum is howeverdifferent from the independent particle case because of the modifying influence ofthe denominator as we will discuss shortly. If the electronic Larmor radius is smalland the ionic Larmor large compared with the density wavelength an exception oc-curs in the rule that the low frequency part of the electronic spectrum is determinedby ion induced electron clouds when β → 90°. The electrons will then be constrainedto move along the field lines and can no longer follow the ion motion across the fieldlines. This will begin to affect the ion-induced spectrum when:

vth cos β ≅ Vth or when cos β = Vth

vth =

θi

θe

1/2

m

M

1/2 (63)

The last of the ion-induced spectral lines will have vanished from the spectrumwhen

kvth . cos β ≅ Ωi

4 or when cos β ≈ 1

2 2kRi

θi

θe

1/2

m

M

1/2 (64)

When cos β is smaller than this limiting value the spectrum is a single large peakround ω = 0. For frequencies in the range kVth < ω < kvth the spectrum is essentiallydue to dressed electrons. As we have seen the spectral density is here usually consid-erably lower than in the ion-induced region.

We now study the properties of the denominator. The most prominent feature isthe plasma resonance. This arises as follows: when kDe is small, X = ω/kvth must be

large for χ to approach unity. This occurs at such a high frequency that the ion termis essentially zero in the denominator. The first term in an asymptotic expansion forχe for large ω in the absence of a magnetic field is:

χ → - 1(kDe)2 (X-2 + 3 X-4 + 15 X-6 ... (65)

The denominator therefore vanishes when:

ω = ωpe (1+1.5(kDe)2) (66)

at this frequency there is a peak in the spectrum corresponding to longitudinalplasma oscillations or Langmuir oscillations. When the scale is decreased or theDebye length increased the plasma resonance effect is washed out because thereal part of χe becomes non-negligible at this frequency. The area under the

25

plasma peak will be so small that the scattered energy will not be appreciable. See adiscussion of this point by Salpeter [1960], and the discussion of photo electron en-hancement below.

We must next discuss the modification on the unperturbed spectra introduced bythe denominator in the low-frequency part of the frequency spectrum, when ω < kVth.

At equilibrium when θe = θi the denominator has a minimum at about ω ≈ 2 kVth.

For frequencies ω < kVth. the denominator is decreasing so that the spectrum is ap-

proximately. At ω ≈ 2 kVth there will therefore be a slight maximum in the spec-trum. With increasing electron temperatures this maximum becomes more pro-nounced because the electron term in the denominator becomes increasingly small.The minimum in the ion function χi never becomes very pronounced, however, sothe ion peak never becomes sharp.

The development so far presented has assumed that the test particles in the plasmatravel along unperturbed orbits, only influenced by the presence of a magnetic field.For a more accurate treatment the effect of the microfield on the orbits must also betaken into account. For the physical conditions in the ionosphere this refinement canbe ignored. An effect which cannot be ignored, however, is the orbital perturbationcaused by the binary collisions in the plasma. In their presence the charged particleswill no longer travel along deterministic paths, but will be subject to probabilisticlaws of motion. The question of type of collisions comes in, whether it is elastic ornot, or in-between, and whether a charge exchange occurs in the collision.

A correct treatment becomes exceedingly complicated and we shall therefore hereonly crudely study the effect of binary collisions by assuming that the particles col-lide elastically with a background of neutral particles, and effectively diffuse throughspace. Such particle diffusion has been studied by Chandrasekar [1943] and others.Adopting this formulation we obtain results which are identical to those obtained byusing a Fokker-Planck collision term in the Boltzmann equation. Other options areavailable, for instance the Bhatnagar-Gross-Krook approximation. The spectra pre-dicted by these methods are nearly indistinguishable as far as their shape is con-cerned, and only show slight variations in the derived apparent collision frequencies.In the Fokker-Planck case, without an external magnetic field all one has to do toderive the power spectra is to replace the correlation function ρ(k,τ) of Eq. 32 in theexpressions for the susceptibilities χ(k,τ) and in the independent particle spectraN°(k,τ) with the expression:

ρ(k,τ) = exp

-

k vth

υc 2

υc τ - 1 + exp( - υc τ ) (67)

26

where υc is the collision frequency in this model. The distortion in the ion spectra fora thermal equilibrium plasma for various values of the normalised ion-neutral colli-sion frequency Xi = υi / k Vth for a fixed value of Xp = ωpe / k vth is shown in figure 8.As can be seen increasing collision frequencies cause the spectra to narrow and be-come more Gauss-like.

The case of multiple ion species is also of importance as there is a tendency in theionosphere for the lighter mass ions to be found at the highest altitudes, and the tran-sition from one to the other is often of considerable interest. The treatment of thiscase is a relatively trivial extension of what has been presented. One must replace theion components of the spectral expressions, both in χ(k,τ) and N°(k,τ) with weightedmean values of the expressions for the various ion species, making sure that theplasma remains neutral in the mean. Figure 9 shows the spectra for various mixingfraction of oxygen and hydrogen ions. Note that the normalised frequency is referredto the hydrogen thermal velocity VH, i.e. X = ω / k VH. The fraction f refers to thefraction of hydrogen ions.

0 0.5 1 1.5 2 2.5 3 3.5 40

0.5

1

1.5

2

2.5

3

X = 5.0i

X = 1.0i

X = 0.5i

X = 0.1i

X = 0.0i

Normalized Frequency

Spe

ctru

m (

Dyn

amic

For

m F

acto

r)

Figure 8. Ion power spectra for thermal equilibrium for various values of ion-neutral collision fre-quencies expressed as Xi = υi / k Vth for a fixed value of Xp = ωpe / k vth.

27

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 510

−4

10−3

10−2

10−1

100

101

f=0.0 f=0.05

f=0.5

f=1.0

Normalized Frequency

Spec

trum

(D

ynam

ic F

orm

Fac

tor)

Figure 9. Ion power spectra for a mixture of hydrogen and oxygen ions. The mixing ratio

f = NH / (NH + NO). Note that the normalized frequency X refers to hydrogen, i.e. X = ω€/€kVH.

Finally let us briefly touch the problem of computing the total scattered power.This has been done by Buneman [1962] and we only briefly give the results here forcompleteness. The total fluctuation caused by dressed electrons and by the ion in-duction are treated separately. For the electron contribution it is argued that k Ti ≈ 0over the larger portion of the frequency range contributing. Using this simplificationintegration over ω shows:

1

2π ⌡⌠

Φ(k,ω) dω

electrons ≈

(kDe)2

1 + (kDe)2) (68)

In the low frequency range where ion dynamics are important the integration is

carried out by putting k Te = - i. The result is:

1

2π ⌡⌠

Φ(k,ω) dω

ions ≈

1[(kDe)2 +1] [(kDe)2 +1+θe/θi]

) (69)

28

It is not quite clear how accurate these results are in general. However, they do re-duce to the correct values for equal temperatures θe = θi. In this case the total fluc-tuation may be derived directly from thermodynamic arguments, see Fejer [1960],Hagfors [1961].

It is in most cases very difficult to detect a well developed plasma line because thetotal power is proportional to (kDe)2, which must be small for Langmuir waves toexist. The exitation of Langmuir waves can, however be strongly enhanced by thepresence of a tail of suprathermal electrons caused either by photo electrons createdin the production process of the ionospheric plasma through solar ultraviolet radia-tion, or through the precipitation of energetic charged particles at high latitudes. Asa model of the suprathermal electrons we shall assume a Maxwellian distribution at atemperature θ1 and with a density which is a small fraction f of the total electrondensity Ne. Using the simple expression for the power spectrum near the plasma lineas derived from Eq. 16 we obtain:

Φ(k,ω) = VNe |1 + χi(k,ω)|2 Φ0e(k,ω)

|1 + χe(k,ω) + χi(k,ω)|2 (70)

Assuming that we are in the parameter regime which corresponds to well definedplasma oscillations at the Langmuir frequency ωL ≈ ωp (1+1.5 (kDe)2) the real partof the ion susceptibility is on the order kDe (m/M)3/2 and can be ignored. What re-mains of the spectrum becomes:

Φ(k,ω) = VNe Φ0e(k,ω)

|1 + χe(k,ω)|2 (71)

Expanding the denominator about the resonance frequency ωR to second order in

ω-ωR and making use of the expression for the susceptibility in terms of the G(ω) weobtain for the total power in each of the two plasma lines:

Φ(k)= VNe

ωp4

d2GI(ω)

dω2

-1

d2GR(ω)

dω2

-1 GR(ω) (72)

In this equation we have put:

G(ω)=GR(ω) + i GI(ω)

For a Maxwellian plasma without magnetic field and collisions we have:

29

GR(ω) =π2

1k e-½X2 for all X

GI(ω) =1k (X-1 + X-3 + 3 X-5 ...) X » 1 (73)

GI(ω) =1k (X -

13 X3 +

15 X5 ...) X « 1

and X=ω/kvth. With two overlapping electron Maxwellian velocity distributions at

different temperatures and different densities, one for the background at density (1 - f) Ne and temperature θ1, and the other for the photo electrons with density f Ne and

temperature θ2, one obtains:

G(ω)= (1 - f) G1(ω) + f G2(ω) (74)

where f is the fraction of the electron density carried by the photo electrons, θ1 the

temperature of the thermal electrons and θ2 the temperature of the photo electrons.The functions G1 and G2 are found by substituting the appropriate temperatures intothe G-functions defined above.

Figure 10. Plasma line enhancement factor plotted against the fraction of photoelectrons f and

T= θ2/θ1 where θ2 is the temperature of the photoelectrons and θ1 the temperature of the back-

ground.

30

Figure 10 shows the normallized plasma line radar cross section as a function ofthe fraction f of photo electrons, and the temperature ratio θ2/θ1 for two differentvalues of kDe=1/Xp. As can be seen the plasma line enhancement can be quite sub-stantial when photo electrons, or other suprathermal electrons are present. Because ofthe limited sensitivity of the ISR installations plasma line observations are nearlyalways made when there is a substantial enhancement. From such observations the"temperature" and the density of suprathermal electrons may be assessed.

4. - ConclusionIn the present report we have rederived and extended certain well known expres-

sions for the scattering of electromagnetic waves by thermal electron density fluc-tuations in a plasma. The derivation was based on a first order solution of the Vlasovequation in a homogeneous plasma with an external magnetic field present. In thederivation the concept of superposition of dressed particles as introduced into plasmaphysics by Rosenbluth and Rostoker [1962] was exploited fully in order to stress thephysical processes determining the properties of the thermal fluctuations. The resultscan be used in non-equilibrium situations where electrons and ions are at differenttemperatures but individually in equilibrium. The method can also be used to studynon-Maxwellian plasmas provided they are not unstable.

It was also indicated how in the same framework transverse electromagnetic parti-cle interaction can be taken into account. This was not developed in much detail,however, because such interactions are not of much interest in the interpretation ofscattering from the ionosphere.

The foregoing discussion is believed to present a fairly complete picture of thepresent state of development of the theory of density fluctuations in the ionosphericplasma. Further problems that obviously must be studied more closely in future arethose relating to instabilities caused by currents passing through the ionosphere, andthose connected with the fact that the ionosphere is only partly ionized and thattherefore collisions play some part in determining the fluctuations, and must be con-sidered in greater detail.

Acknowledgement:

The author has benefited greatly from cooperation and discussions with Dr. Buneman and Dr.Eshleman of Stanford University during the initial phases of this work, and later through numerousEISCAT colleagues. Dr. Galina Sukhorukova has carried out the numerical calculations for theillustrations.

31

5. ReferencesBeynon W.J.G., P.J.S. Williams, Incoherent scatter of radio waves from the iono-

sphere, Rep. Prog. Phys., 41, 909-956, 1975.

Bowles K.L., Observations of vertical incidence scatter from the ionosphere at 41Mc/s, Phys. Rev. Letters, 1, 454, 1958.

Bowles K.L.,Incoherent scattering of free electrons as a technique for studying theionosphere and exosphere: Some observations and theoretical considerations, J.Res. N.B.S., 65D, 1, 1961.

Bowles K.L., G.R. Ochs, J.L. Green, On the absolute intensity of incoherent scatterechoes from the atmosphere, J. Res. N.B.S., 66D, 395, 1962.

Buneman O., Fluctuations in a multicomponent plasma, J. Geophys. Res., 66, 1978-1979, 1961.

Buneman O., Scattering of radiation by the fluctuations in a nonequilibrium plasma,J. Geophys. Res., 67, 2050-2053, 1962.

Chandrasekhar S., Stochastic problems in Physics and Astronomy, Rev. Mod.Phys., 15, 1-89, 1943.

Dougherty J.P., D.T. Farley, A theory of incoherent scattering of radio waves by aplasma, Proc. Roy. Soc., 259A, 79-99, 1960.

Dougherty J.P., D.T. Farley, A theory of incoherent scattering of radio waves by aplasma, 3. Scattering in a partly ionized gas, J. Geophys. Res., 68, 5473-5486,1963.

Evans J.V, Theory and practice of ionosphere study by Thomson scatter radar,Proc.IEEE, 57, 496-530, 1969.

Farley D.T., J.P. Dougherty, D.W. Barron, A theory of incoherent scattering ofradio waves by a plasma, 2. Scattering in a magnetic field, Proc. Roy. Soc., 263A,238-258, 1961.

Fejer J.A., Scattering of radio waves by an ionized gaz in thermal equilibrium, Can.J. Phys., 38, 1115-1125, 1960a.

Fejer J.A., Scattering of radio waves by an ionized gaz in thermal equilibrium in thepresence of a uniform magnetic field, Can. J. Phys., 39, 716-740, 1961.

Gordon W.E., Incoherent scattering of radio waves by free electrons with applica-tions to space exploration by radar, Proc. I.R.E., 46, 1824-1829, 1958.

32

Hagfors T., Density fluctuations in a plasma in a magnetic field with applications tothe ionosphere, J. Geophys. Res., 66, 1699-1712, 1961.

Millman G.H., A.J. Moceyunas, A.E. Sanders, R.F. Wyrick, The effect of Faradayrotation on incoherent backscatter observations, J. Geophys. Res., 66, 1564-1568,1961.

Moorcroft D.R., On the determination of temperature and ionic composition byelectron backscattering from the ionosphere and magnetosphere, J.Geophys Res,69, 955-970, 1964.

Perkins F.W., E.E. Salpeter, K.O. Yngvesson, Incoherent scatter from plasma os-cillations in the ionosphere, Phys. Rev. Letters, 14, 579, 1965.

Pineo V.C., L.G. Kraft, H.W. Briscoe, Ionospheric backscatter observations at 440Mc/s, J. Geophys. Res., 65, 1620-1621, 1960.

Renau J., Scattering of electromagnetic waves from a nondegenerate ionized gas, J.Geophys. Res., 65, 3631-3640, 1960.

Rosenbluth M.N., N. Rostoker, Scattering of electromagnetic waves by a nonequi-librium plasma, Phys. Fluids, 5, 776-788, 1962.

Salpeter E.E., Electron density fluctuations in a plasma, Phys. Rev., 120, 1528-1535,1960.

Salpeter E.E., Plasma density fluctuations in a magnetic field, Phys. Rev., 122,1663-1674, 1961.

Sheffield J., "Plasma Scattering of Electromagnetic Radiation", Academic Press,New York, San Fransisco London, 1975.

Sitenko A.G., "Electromagnetic Fluctuations in Plasmas", Academic Press, NewYork, London, 1967.

Woodman R., Incoherent scattering of electromagnetic waves by a plasma, Thesis,Harvard, 1965.

33

PLASMA INSTABILITIES AND THEIR OBSERVATIONS WITHTHE INCOHERENT SCATTER TECHNIQUE

Wlodek Kofman

1. IntroductionThis chapter deals with the presentation of non-linear processes in the auroral

ionosphere which are observable by the incoherent scatter technique. These non-linear phenomena can be directly seen on the shape of the spectrum or indirectlyon the ionospheric parameters. In a first part, one starts with the simplified, classi-cal and linear description of the wave modes in the plasma. The concept of theunstable waves which can grow in space and/or in time is then introduced in thesecond part. These are the normal modes of plasma which, in the presence of the"free energy" source, become unstable. These modes have a well-defined relation-ship between the κ vector and the angular frequency ω which implies that theplasma fluctuations are weak. The quasi-linear theory is suitable to outline thephysics. We use this quasi-linear description of the waves in the plasma in orderto derive the instabilities measurable by radars. In the third part, illustrations aregiven with incoherent scatter measurements and various auroral processes; "freeenergy" sources responsible for these instabilities like electric convection fieldand precipitations are discussed.

2. Waves in the plasma.In this chapter, the simplified theory of the plasma waves is developed using

two approaches : fluid and kinetic, this in order to introduce the normal modes inthe plasma, which are usually observed with the incoherent scatter technique.These modes are unstable in some situations; their description is the goal of thispaper.

2.1. Fluid equationsThe total charge and the current density in the plasma are described by the fol-

lowing equations :

ρ = ni qi + ne qe

j = ni qivi + ne qeve (1)

In this description, we do not use a single particle motion but the fluid velocityv which corresponds to the average velocity of particles.

34

The Maxwell equations describe the relations between the electric and themagnetic fields in the plasma, respectively E and B.

ε0 ∇ E = ρ∇ B = 0

E = – ∂ B∂ t

µ-1 B = j + ε0 ∂ E∂ t

(2)

where subscripts ε0 and µ represent the dielectric constant and the permeability,respectively, and j is the current density.

To obtain the fluid description, one has to introduce the momentum and conti-nuity equation in addition:

mj nj

∂ vj

∂ t + (vj) vj = qj nj ( E + vj B ) - ∇ pj

∂ nj

∂ t + ∇ ( nj vj ) = 0

(3)

where subscript j corresponds to ions and electrons; m, n, v and q are the particlemass, density, velocity and charge, respectively; pj = Cj njc is the thermodynamicequation of state with c being the ratio of specific heats, and Cj is constant. Ingeneral, P is a stress tensor which, for the Maxwellian plasma, takes the form of adiagonal matrix with the same elements pj. In this case, one obtains . P = ∇ pj.

For the isothermal plasma c = 1 and in more general cases c = 2 + N

N where N is

the number of degrees of freedom of the gas, c = 3 for one dimensional adiabaticcompression.

The solution of these equations gives a self-consistent set of fields and motionsin the fluid approximation.

In a plasma, it is usually possible to assume ni = ne and ⋅E ≠ 0 at the sametime. One calls this approximation a quasi neutrality. As long as motions [waves]are slow enough for both ions and electrons to have time to move, it is legitimateto replace Poisson equation by ni = ne. If it is not the case, one has to find E fromMaxwell equations.

35

The traditional development of the linear theory of waves in the plasma is theapplication of the Fourier/Laplace analysis in space/time, in which one assumesthat the fluctuations are in the following form :

n = n1 exp[ j ( . r -ω t )]

E = E1 exp[ j ( . r -ω t )](4)

where is a wave vector, r is a position and ω an angular frequency. From themomentum and continuity equations, the fluctuating particle densities and currentdensities are obtained and are then inserted into Maxwell equations to obtain adispersion equation. This equation relates ω and and therefore determines nor-mal modes of plasma. This global and full dispersion equation obtained from thewhole set of linearised equations has a complicated form. The various approxi-mations can be derived from this general solution giving modes of the plasma. Inthis chapter, we adopted a different approach using the suitable assumption in or-der to start with simplified equations.

The dispersion equation may be solved either as a boundary value problem [ωreal and κ complex] or as an initial value problem [κ real and ω complex]. In thispaper, we will use the latter approach. We will suppose ω = ωr + j γ , where γ is a

growth or dumping rate. For γ > 0, the plasma is unstable. For the Maxwellianparticle distribution, the dispersion equation typically yields non growing modes.The "free energy" [anisotropy, inhomogeneity, relative drift between differentspecies] is necessary to produce instabilities.

The weakness of the fluid approach is that one can include the damping[growth] rate depending only on collisions.

From the point of view of the analysis, it is advantageous to separate the fluc-tuations fields into two types :

• longitudinal: E = 0

• transverse: . E = 0

The plasma fluctuations that only have a longitudinal component have no mag-netic field [B = 0] and are named "electrostatic". Indeed, the complete solution ofthe general dispersion equation will typically have contributions from two fields :transverse and longitudinal. The transverse component is a purely electromagneticone. Most fluctuations in space plasmas have both components.

36

2.1.1. Electron plasma wave.To analyse the electron plasma waves, let us imagine that the ions form a uni-

form background. If the electrons are displaced by some perturbation, an electricfield will build up in such a direction as to restore the neutrality. Because of theirinertia, the electrons will overshoot and oscillate around their equilibrium posi-tions. We are presently interested in the fast oscillations [ω > κ (k T / me)1/2]. Themassive ions do not have time to respond to the oscillating field and it is why theymay be considered as fixed. To simplify, let us assume that the motion only oc-curs in one direction.

In this chapter, we are interested in the electron plasma waves which are theelectrostatic mode. The condition according to which the electric field is parallelto the κ vector leads to the application of only the Poisson equation from the setof Maxwell equations [B = 0, E = 0]. Therefore, we have a set of followingequations.

me ne

∂ ve

∂ t + (ve) ve = - e ne E - ∇ pe

∂ ne

∂ t + ∇ ( ne ve ) = 0

ε0 . E = e ( ni - ne)

(5)

where subscripts e and i stand for electrons and for ions, respectively.

As we said before, the replacement of the Poisson equation by ni = ne is possi-ble in the case of slow motions. The electron plasma waves are fast and the den-sity fluctuation occurs.

In the small amplitude approximation, one can linearise equations.

ne = n0 +n1; ve = v0 + v1; E = E0 + E1

One supposes that the uniform field and neutral plasma are at rest at the begin-ning, which leads to the following conditions and equations.

∇ n0 = v0 = E0 = 0 and:

∂ n0

∂ t = ∂ v0

∂ t = ∂ E0

∂ t = 0

me n0

∂ v1

∂ t + (v1) v1 = - e n0 E1 - ∇ pe

∂ n1

∂ t + n0 ∇ v1 + v1 ∇ n0 = 0

(6)

37

The second term in the momentum equation is quadratic in amplitude and welinearise by neglecting it. We did the same for other second order terms [n1E, n1 ∂v1 / ∂ t].

The third term in the continuity equation is zero due to our assumptions.

Applying the Fourier/Laplace method, one obtains the set of equations:

ε0 ∇ .E1 = - e n1

- j κ E1 ε0 = – e n1

- j me v1 n0 ω = – e n0 E1- ∇ pe

– j ω n1 = – n0 j κ v1

∇ pe = c k Te ∇ ne

c = N + 2

N

(7)

with c = 3 for one dimensional problem, and k being the Boltzmann constant.

By eliminating E1 and n1 from the previous equations, the dispersion relationfor electron plasma waves in the fluid approximation is obtained :

ω 2 = n0 e2

ε0 me +

3 k Te

me κ2 (8)

where one terms the plasma angular frequency where n is in m-3 units

ωp2 = n0 e2

ε0 me (rad.s-1)2 and fp ≅ 9 n0 (9)

Defining the thermal velocity as vth2 = 2 k Te

me, this dispersion relation is often

written:

ω2 = ωp2 + 32 κ2 vth2 (10)

This relation is presented in Figure 1 in the ω-κ. coordinates.

38

kVϕVg

Figure 1. Dispersion relation in the ω-κ coordinates, with: vg = dωdκ =

3vth2

2vϕ and vϕ =

ωκ .

For the large κ, vg ≅ vϕ and therefore the group velocity is essentially at thethermal velocity.

Figure 2. Examples of measured upshifted and downshifted plasma lines, with 10-s integrationtime and their fit to the model.

39

The analysis made previously neglected the magnetic field. In the case of thepresence of the magnetic field, which is the case of the ionosphere, equation 8slightly changes. The term depending on the gyrofrequency and on the angle be-tween the κ vector and the magnetic field [ ωc2 sin2θ ] is added to the right side ofthe equation. In this chapter, we analysed the one dimensional motion. In theplasma, the electrostatic plasma waves propagate in all possible directions withthe dispersion relation given previously.

The incoherent scatter technique gives the possibility to observe the plasmawaves. In Figure 2, one shows the measurements of the plasma lines [Kofman etal., 1995] obtained by EISCAT radar. One can see two lines close to ±7.6 MHz,upshifted and downshifted, respectively due to plasma waves going towards andaway from the radar.

The wide spectrum observed [≈ 50 kHz] is due to the technique used in thesemeasurements. For the homogeneous ionosphere, the plasma line is very narrowwith a width of few kHz due to the collisions between electrons and ions, elec-trons and neutrals and Landau damping [see § 2.2.1]. In these measurements, oneused the long-pulse modulation. This implies that the covered ionosphere is nothomogeneous and that the resonance frequency changes inside the radar band-width. The strong peak seen in the figure corresponds to the frequency peak of theF-region. In the ionosphere, there is no higher frequency than this one and this iswhy there is a sharp cut-off on the right [left] side of the upshifted [downshifted]line.

2.1.2. Ion acoustic waves.In the neutral gas, acoustic waves are excited through the normal binary colli-

sions.

In the absence of ordinary collisions, acoustic waves can occur through the in-termediary of an electric field. Ions are massive compared with electrons; theirvelocity is much lower than the one of electrons and therefore acoustic waves arelow-frequency oscillations.

Electrons move much faster than ions, because they are light [≈ 1832 times forprotons] and therefore they can fast respond to the charge separation electric field.When the ions are perturbed, the electrons fast neutralise the perturbation and thismakes the wave propagate.

One can see the acoustic waves in the plasma, like the waves in the neutral gas,where the neutral particles are the ions screened by the electrons. Therefore, in thefluid calculations, one can assume the quasi neutrality ne ≈ ni = n, which meansthat the ions and the electrons fluctuate in the same way.

40

The momentum and the electric field are given by :

mini

∂vi

∂t + (vi) vi = -e n0 ∇ ϕ - ci k Ti ∇ ni

E = - ∇ ϕ(11)

The fluid is accelerated under the combined electrostatic and pressure gradientforces. The electrons move but they cannot leave a region en masse because theywill leave the ions. The electrostatic force, due to the charge separation, and pres-sure gradient force must be closely in balance. This condition leads to the Boltz-mann relation :

n = n0 exp

e ϕ

k Te = n0

1 + e ϕ1

k Te + ... = n0 + n1 (12)

with n1 = e ϕ1

k Te n0 , ϕ = ϕ0 + ϕ1 and ϕ0 = 0 because E0 = 0.

Figure 3. Ion waves spectra measured by incoherent scatter radar.

41

Therefore, the linearised ion equations using the Fourier/Laplace transforma-tion are :

– j ω mi n0 vi1 = – j e n0 κ ϕ1 – j ci k Ti κ n1

– j ω n1 = – j n0 κ vi1(13)

Using equations 12 and 13, one obtains the dispersion relation for ion-acousticwaves.

ω2 = κ2

k Te

mi +

cik Ti

mi or:

ω

κ2 =

k Te + ci k Ti

mi = cs2

cs as defined here is the sound speed.

It is a one dimensional case and therefore ci = 3; for electrons, ce = 1 becausethey are isothermal due to their fast movements relatively to the waves. Basically,ion waves have a constant velocity and vϕ = vg.

The validity of our solution depends on the assumed quasi-neutrality and thisimposes the conditions ( κ λd )2 << 1 where λd is the Debye length, which meansthat this approximation is only valid for long wavelengths. For short wavelengths,the ion acoustic wave turns into a ion plasma wave.

In Figure 3, we show the typical ion spectra [see previous §] measured by inco-herent scatter radar at altitudes of 99 and 105 km. The crosses show the measure-ments and the continuous line the fit by the theoretical function. Those spectra aregenerated by the ion-acoustic fluctuations in ionospheric plasma. One can see thetypical shoulders which are due to ion acoustic waves.

These spectra are typical when the ion temperature is close to the electron one.When the electron temperature is larger than the ion temperature, for instanceTe / Ti ≈ 2 is a very frequent case in the F-region, the shoulders are much morepronounced. The ratio of the value at the maximum of the spectrum to the value atzero frequency determines the temperature ratio. The width of the spectrum de-termines the ion temperature. This dependence is a first order approximation, theionospheric parameters are usually obtained by the fit of the measurements by thetheoretical function on all the various plasma parameters [see chapter by Schlegel,this volume].

42

2.2. Kinetic derivation of dispersion relationsThe alternative approach to study the waves in plasmas, which is probably

richer especially in the description of instabilities, is the kinetic one. In order todescribe the plasma gas, one introduces the single particles distribution functionfj( r , v , t ). From this function, one derives all moments : density, mean velocity,temperature [energy], pressure, etc.. To study the waves in plasmas, one usuallyapplies the Vlasov equation which is derived from the Boltzmann equation in-cluding only electromagnetic interactions. Other types of collisions are neglected.

The Vlasov equation is:

∂

∂t + v .

∂∂r +

qj

mj (E + v x B)

∂∂v fj( r , v , t ) = 0 (15)

The fields E and B are the sum of those applied from outside sources and thoseincluded from collective motion of plasma particles. For the longitudinal waves,E can be determined using only the Poisson equation :

ε0 .E = ρext + Σj ⌡⌠qj nj fj dr (16)

To obtain the dispersion relation, one needs to substitute the perturbation in theVlasov equation :

fn = f0 + ∆ f exp( )j(.r -ω t)

E = E0 + ∆ E exp( )j(.r -ω t)B = B0 + ∆ B exp( )j(.r -ω t)

(17)

where f0 is the equilibrium distribution function, ∆f, ∆E and ∆B are perturbations[assumed to be sinusoidal in order to apply a Fourier/Laplace analysis] and n isthe density.

2.2.1. Electrostatic wavesFrom the Vlasov and Poisson equations, one obtains the set of equations for the

electrostatic waves.

∆ f =

-q∂ fm∂ v ∆ E

j (v. - ω)

∇ E = ρε0

⇒ E () = – j κ2

ρ()ε0

∆E = q2 n

ε0 m κ2 ⌡⌠

∂f∂v

v. -ω dv . ∆E

(18)

43

The first equation is obtained after the linearisation of the Vlasov equation. Thesecond is the Poisson equation. To obtain the third equation, the fluctuation of thecharge density was obtained by the integration of the ∆f over the velocity spaceand by the introduction into the Poisson equation. Thus:

1 = ωp2

2 ⌡⌠

∂f∂v

v. -ω dv, with:

ωp2 = q2 nε0 m

(19)

One names the dielectric function for longitudinal fluctuations the followingquantity :

ε ( , ω ) = 1- ∑j

ωj2

κ2 ⌡⌠

∂fj∂v

v. -ω d v (20)

This form of dielectric function is only valid in the absence of magnetic field orin the direction parallel to the magnetic field, // B0.

This equation is difficult to evaluate in a simple way because of the existenceof a singularity at ω = v.. The proper treatment of this problem was done byLandau in 1946 and this lead to the concept of the Landau damping of the waveswhich is a non-collisional damping. This problem is discussed in many text booksand this is why we will here only summarise the results for studied waves.

In the case of the Maxwellian distribution of the particles, the dielectric func-tion takes a special form.

ε ( , ω ) = 1 + ∑j

κj2

κ2 W(ω

κ Tj/mj) (21)

with κj2 = n q2

ε0 Tj [where Tj is the temperature expressed in energy units], and

W(z) = 1

2 π ⌡⌠

c

xx-z exp( -

x2

2 ) dx)) is the Fried-Comte function.

44

The plasma modes correspond to the solutions for ω€( κ ) of the equationε ( , ω ) = 0.

2.2.2. Collective ModesThe simplest type of collective modes in the plasma is the electrostatic plasma

wave. If one supposes that the plasma is only composed of electrons, the disper-sion relation is given by Eq. [22].

1 + κe2

κ2 W

ωκ Te/me

= 0 (22)

For high frequencies for which the condition ω

κ Te/me >> 1 is fulfilled, one

can use the asymptotic development of W. The formula ωκ2 ≅ ωp2 +3 Tm κ2 gives

the solution of the real part of Eq. [22]. This describes the same mode as the onefound in the fluid approximation.

The dispersion relation was solved supposing κ real and ω complex. Each ωmode has an imaginary part and this means that the fluctuations are damped orcan grow. In this case, the imaginary part given by :

γκ = -

π8

1/2 ωp

κe3

κ3 exp

- ωκ2

2 κ2 (T/m) (23)

describes the Landau damping of the waves. Figure 4 shows the customary physi-cal picture of the Landau damping. The particles which move faster than the wavegive energy to the wave and the particles which move slower damp the wave. Thismeans that if there is locally a positive slope in the particle distribution function,near the phase velocity of the wave, the amplitude of the wave can grow. In thiscase, the number of particles moving faster than the wave is larger than thosemoving slower. The value of the damping depends on the derivative of the distri-bution function at the phase velocity.

Figure 4. Customary physical picture of Landau damping.

45

2.2.3. Ion-Acoustic WavesThis mode is obtained for the plasma composed of ions and electrons. The dis-

persion relation Eq. [21] developed in the frequency range

κ

Te

me

1/2 >> ω >> κ

Ti

mi

1/2 gives the resonance frequency and the growing rate

given by Eq. [24]. This is a normal ion-acoustic mode which is strongly dampedwhen Te is close to Ti. The normal incoherent scatter spectrum corresponds tostrongly damped waves.

ωκ =

Te

mi +

3Ti

mi

1/2κ

γκ = -

π8

1/2

me

mi

1/2 +

Te

Ti

3/2 exp

- Te

2 Ti -

32

(24)

3. InstabilitiesThese are normal modes of a plasma that grow in space and/or in time and that

have the following properties :

[1] relations between κ and ω are well defined, which means relativelyweak fluctuations

[2] macro instabilities depend on the space properties of plasma[3] micro instabilities are driven by the departure from the equilibrium of the

plasma distribution

The border between these two categories is not clearly cut.

Due to the previous remarks and the Fourier/Laplace approach used in thisanalysis of the weak instabilities, the normal modes are usually described as planewaves: n ∝ n1 exp[ j ( .r - ωκ t ) ]. The usual Maxwellian distribution, due to thefact that its derivative is always negative, leads to non-growing modes. In order toyield instabilities, the modification of the distribution function from the one atequilibrium should occur and this needs a "free energy". This "free energy" comesfrom different sources like anisotropy of particles, relative drift in the ionosphereor the inhomogeneity of the plasma.

For instance, the instability can be caused by the plasma density gradient andthis is a large-scale phenomenon.

46

Figure 5. Beam-plasma instability

3.1. Beam-Plasma InstabilityTo study the beam-plasma instability, one assumes, for a simplified analysis,

the plasma to be cold and uniform. This means that the temperatures fulfilTi ≈ Te ≈ 0. Therefore, fluid and kinetic descriptions give the same answer. Theelectrons are assumed drifting through ions with the velocity vD. These two as-sumptions lead to the Dirac distribution function.

f(v) = ni δ i (v) + ne δ e (v - vD) (25)

47

The dielectric function is obtained from the previous general formula in a sim-ple way using the properties of the delta function.

ε ( κ , ω ) = 1 - ωi2

ω2 - ωe2

(ω - κ vD)2

ω2J = n e2

ε0 mj [where j stands for ions and electrons]

x = ωωe

and y = κ vD

ωe

1 =

me

mi .

1x2 +

1(x - y)2 = F(x,y)

(26)

The last equation can be solved to find the ion plasma modes. As shown in fig-ure 5, there are two possible situations. The solution consists of four real rootswhich correspond to the stable plasma [Fig. 5a,b] or of two real and two complexroots which are the case of the unstable plasma [Fig. 5c], due to the imaginarypart of the roots. These two complex roots are conjugated and this gives onedamped and one growing mode. The maximum growth rate is given by the fol-lowing formula :

γ ≅ ωe

me

mi

1/3 (27)

From Figure 5, one can see that for sufficiently small y, which means for long-wavelength waves, the plasma is unstable.

This cold plasma approximation does not take into account the Landau damp-ing and is good for the situations in the presence of fast streaming electrons.

3.2. Ion-Acoustic InstabilityThe conditions for the ion acoustic instability taking into account the Maxwel-

lian plasma can also be easily derived in the direction parallel to the magneticfield. The "free energy" is the electron drift vD relative to ions as previously. One-dimensional distribution functions are introduced into the equation for the dielec-tric function.

fe(v) = 1

2π Τe/me exp

-

(v-vD)2

2 Τe/me

fi(v) = 1

2π Τi/mi exp

-

v2

2 Τi/mi

ε (κ,ω) = 1 + κe2

κ2 W

ω - κvD

κ Te/me +

κi2

κ2 W

ω

κ Ti/mi

(28)

48

Figure 6. The threshold drift as a function of electron temperature and electron density. Iontemperature was fixed at 1000°K. For instance, for ne=6 1011 m-3 and Te ≈ 6000°K, the thresh-

old drift is 40 km.s-1.

For ion acoustic waves, one has searched for the solution with the wave speedfulfilling the following condition :

Ti / mi << ω κ

<< Te / me + vD (29)

The solution of the dispersion equation is :

ωκ = ± ωi κ

κ2 + κe2

ω i 2 = n e2

ε0 mi

γ κ ≅ -

π8

1/2

me

mi

1/2 κ

(cs - vD) + cs

mi

me Te3

Ti3 exp( -

Ti

2Te)

(30)

The physical description of the process is the following : the drift motion ofelectrons relative to ions interacts with one acoustic mode which lifetime in-creases. The other mode on the contrary is strongly damped. When the velocityincreases, one mode can become unstable.

The acoustic waves are unstable when vD > cs and strongly depend on the tem-perature ratio Te / Ti. In figure 6 we show how the threshold drift, corresponding

to γ κ = 0, for the unstable acoustic waves depends on the temperature ratio and on

the electron density for a vector of the EISCAT UHF radar. These are the exactcalculations for the threshold. One can see that the drift velocity necessary to de-stabilise the plasma diminishes with the electron temperature. One

49

needs a very large drift velocity of electrons for the EISCAT vector to destabi-lise the plasma.

When the drift velocity is larger than the thermal velocity [ vD > vth ], the coldplasma regime and the fluid description work well and this instability is oftencalled two-stream instability.

3.3. Two-stream InstabilityThis instability is strongly aspect angle dependent [ see Farley, 1963, Fejer and

Kelley, 1980]. The resonance frequency and the growing rate are given by thefollowing formula in the fluid approximation :

ωκ = ( vDe + ψ vDi)

1 + ψ

γ = 1

1+ψ

ψ

vi [ ](ωr - .vDi) - κ2 cs +

1LN κ2

(ω - .vDi)

vi

Ωi.κ -2 α N0

(31)

with:

ψ = ve vi

Ωe Ωi

κ⊥ 2

κ2 + Ωe2

ve2 κ//2

κ2

LN = ne

∂ne

∂z -1

cs =

Te + Ti

mi

1/2

(32)

where vDe is the electron drift velocity, vDi the ion drift velocity and LN the hori-zontal [North-South] gradient of the electron density.

Farley and Buneman [1963] have shown that waves are unstable in a cone ofangle ϕ for which vDe cos ϕ > cs.

For smaller drift velocities, the plasma can still be unstable provided there is aplasma density gradient. The two-stream instability is more important at shortwavelengths, while the gradient drift and recombination instabilities are more im-portant for long wavelengths.

50

Figure 7. Example of five complex autocorrelation functions and the corresponding spectra forincoherent and coherent scatter echoes measured at 105 km altitude from Sodankylä. The arrowabove the spectra shows the mean Doppler shift, the number on the right-hand side of the spec-tra indicates the logarithm of the volume backscatter cross section in m -1.

4. Radar Measurements

4.1. Two-stream InstabilityThe classical incoherent scatter radar theory was studied by Hagfors, [this vol-

ume]. During the observations of plasma irregularities, the much stronger scatter-ing occurs due to enhanced non-thermal plasma density fluctuations. Radars

51

only detect one particular Fourier component corresponding to the wave vectorequal to the difference between the wave vector of the transmitter and the wavevector of the receiver. The density irregularities are strongly field aligned whichrequires measurements with a wave vector perpendicular to the magnetic field.Usually these non-thermal fluctuations are observed with radars using much lowerfrequencies [ten to few tens of MHz] than incoherent scatter radars. One calls thistype of radars "coherent radar". EISCAT observations of two-stream instabilitiesare rare and were made for the first time by Schlegel and Moorcroft [1993]. Fig-ure 7 shows some of these measurements. The spectral form of the narrow coher-ent echoes can be clearly seen in this figure. The authors have compared the crosssections of the different types of scattering: entirely coherent to almost totally in-coherent [figure 8]. The cross section varies of more than two orders of magni-tude. The echoes due to the scattering on the two-stream instability are muchstronger. As it is shown in the theory, the cross section depends on the aspect an-gle and this dependency was studied by the authors.

Figure 8. Scattering cross sections obtained from the Tromsö 360-µs pulse data during the co-herent scatter experiment on May 18-19, 1988. Observations were made at four different eleva-tion angles of the Tromsö antenna, as indicated by the different symbols. The two horizontaldashed lines separate regions where the scattering is almost entirely coherent (above the upperline) and where the scattering is almost totally incoherent (below the lower line).

52

Figure 9. A sequence of 5 successive 10-s data intervals showing how the long-pulse spectrachange from normal to anomalous and back again.

4.2. Anomalous spectraPowerful spectra with strongly asymmetric features [Figures 9 and 10] have

now been unambiguously observed with incoherent scatter radars both at UHFand VHF frequencies [Foster et al., 1988; Rietveld et al., 1991; Collis et al.,1991; Wahlund et al., 1993; Forme et al., 1993; Cabrit et al., 1995]. In all thecases cited here, all these "coherent spectra" feature one strong ion-acoustic peak.These echoes were observed along the magnetic field lines for altitudes rangingfrom the topside ionosphere all the way down to 140 km. Even though this wasquite a unique event, the fact that the observations were made down to 140 km -analtitude where the collision frequency is very large- indicates that these echoes areproduced by the electrons streaming up or down the magnetic field lines, at leastat times. There is also some evidence [Collis et al., 1991, Cabrit et al., 1995] thatthe echoes can clearly come from the boundaries of arcs as opposed to the centresof the arc, at least at times [Fig. 10].

53

Figure 10. Upper panel : Field-line location (km north of radar) of maximum 630 nm intensityfrom the scanning photometer (+) in relation to upshifted (♦ ) and downshifted (o) spectral en-hancements detected by EISCAT on 11 January 1989. Lower panels : Radar spectra showingupshifted (1714:10 to 1714:20 UT, left) and downshifted (1715:00 to 1715:10 UT, right) en-hancements, contrasted with normal spectra (1714:20 to 1714:30 UT, centre). Amplitudes arenormalised to the maximum in each stack, in the ratio 5:1:4, left to right.

The main characteristics of the observations can be summarised as follows :

[1] one of the ion-acoustic shoulders of the incoherent spectra is strongly en-hanced. At some altitudes, both sides of the spectrum can be simultaneouslyenhanced during the time taken by the radar to integrate its signal;

[2] the power of the observed spectra is usually strongly enhanced. This meansthat the radar cross section can be clearly larger than the classical one associ-ated with quiescent plasmas [Figure 11];

[3] the observations are recorded in directions that are close to parallel to themagnetic field line. There are however observations made in the direction at27° to the magnetic field [Cabrit et al., 1995];

54

[4] some of the observations show a reversal in the sign of the enhanced shoulderoccurring at some altitudes [approximately around 200 km];

[5] the statistics seem to indicate that the upper shoulder [ion-acoustic waves go-ing down] is more frequently enhanced than the lower shoulder at altitudesbelow 300 km. Conversely the lower shoulder is enhanced more frequently ataltitudes exceeding 450 km [Rietveld et al., 1991]. Finally, at least for the sub-set of events studied by Rietveld et al. [1991] between 300 and 450 km, neithershoulders dominated the statistics.A theoretical explanation for the generation of these echoes is still a matter of

debate. Two main classes of physical processes have been advanced so far. Thefirst such class relies on relative drifts between the thermal species in the plasmato excite the unstable waves, following a mechanism first proposed by Kindel andKinnel [1971] for the destabilisation of ion acoustic waves along the magneticfield. In that original paper, the destabilisation was done by electrons driftingthrough a stationary background of ions. Rietveld et al. [1991] and St.-Maurice et

Figure 11. Power profiles obtained from 10-s intervals. The thin lines in the two left-hand pan-els show equivalent electron density variation (uncorrected for temperature), while the thicklines show the enhanced echoes from the long-pulse spectra. The two right-hand panels are thecorresponding data for the low altitude, high resolution multipulse channel. Note the enhance-ments which reach a factor of 50 in the lower left panel.

55

al. [1996] used this mechanism by producing ionospheric currents in response tothe magnetospheric generator. In one case, the generator was provided directlythrough an intense precipitation of soft to medium energy electrons from themagnetosphere. As these electrons were stopped by the neutral atmosphere, thedivergence in the currents carried by the precipitating electrons was given tocharged carriers from the thermal part of the plasma which then provided currentclosure. It has been assumed by Rietveld et al. [1991] as well as by St.-Maurice etal. [1996] that in the regions where these currents flow along the magnetic field,they would be carried by thermal electrons. St.-Maurice et al. [1996] have alsoproposed that intense conductivity gradients in the presence of strong ambientelectric fields could also drive intense thermal currents along segments of themagnetic field, although a preconditioning of the plasma through some wave-induced enhancement in perpendicular conductivities [perhaps due to cyclotronturbulence] would be required for this mechanism to have a realistic chance tosucceed. On the other hand, this mechanism would nicely explain the occurrenceat times of echoes organised according to their position with respect to the gradi-ent of arcs.

The main problem with the thermal current mechanism is that it requires verylarge parallel electric fields and, consequently, intense parallel current densities inorder for the plasma to be destabilised under the conditions that exist near the re-gions of observations. Specifically, the required current densities would have tobe of the order of 1 mA.m-2, which has never been reported with direct observa-tions. In fact, the modification of the ion velocity distribution in the presence ofthe strong ambient electric field, can lead to smaller than 1 mA.m-2 value of re-quired current density [Cabrit et al., 1995]. More recent observations from satel-lites have so far pointed to the existence of current densities of the order of100 µA.m-2, which is still an order of magnitude less than required with the ther-mal current theory. However, another order of magnitude in parallel current den-sities cannot be ruled out, as long as the structures that carry these currents arenarrow enough. One could think, for example, of small structures 100 meters inwidth, aligned in the north-south direction [these have been observed with differ-ent instruments] with short-living bursts existing on a time scale of the order of1 ms to 1 s.

A completely different approach has also been proposed by Forme [1994]. Inthis case, the ion-acoustic waves would be produced by the non-linear cascade ofelectron plasma waves, using an analogy from the artificial ionospheric heating byelectromagnetic waves. According to this scenario, low energy precipitating elec-trons would first excite electron plasma waves, which by cascade would then pro-duce secondary plasma and ion-acoustic waves. This mechanism would be verysuccessful at reducing the parallel current thresholds, but it has some difficultiesin explaining how one can observe an upshifted ion-acoustic shoulder en-

56

hancement in the spectrum at times, and a strongly down-shifted structure at othertimes. Some experimental confirmation of the reality of this process in natural io-nospheric situations should be feasible, through the observation of the behaviourof plasma lines during disturbed events, using the same incoherent scatter tech-nique that is used to get the ion line [i.e. the part of the spectrum that we havediscussed so far].

Figure 12. E region spectra from March 18, 1978, obtained with the multipulse autocorrelatorusing a 60-µs unipulse followed one interpulse period later by a burst of three 60-µs pulses thatstarted at 0, 100 and 340 µs. The spectral window is 50 kHz wide. The two time periods wereselected, in part, because of similar signal-to-noise ratios. (a) Typical spectra measured be-tween 1326 and 1331 UT. (b) Unusual spectra measured between 1432 and 1438 UT. In par-ticular, they are unusual at 105 and 110 km, though at 116 km the spectrum is still considerablywider than that in the earlier time period.

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Figure 13. Ion (full lines) and electron (dashed lines) temperature profiles for selected times.There is no anomalous heating at 19.18 UT (left panel), very strong anomalous heating at 01.43UT (centre panel), and low anomalous heating at 02.58 UT (right panel).

4.3. Electron heating by plasma waves.The first observations of very large electron temperatures in the auroral

E-region were made by Schlegel and St.-Maurice [1981) and Wickwar et al.[1981]. These phenomena have since been observed repeatedly. We note thatwhile the data base is now relatively large as a result of years of observations,details about the theoretical explanation are still undergoing some discussions. InFigure 12, one can see the spectra measured in the E region for two periods. Thespectra at 105 and 110 km [first panel] are typical of quiet conditions while theothers [second panel] have a very unusual shape for the E-region [Wickwar et al.,1981] since it has to be clearly associated with very large Te, as indicated by thehigh "shoulders" in the spectrum.

In Figure 13, we show profiles of Te and Ti for three different periods obtainedon the same day. During the anomalous heating event shown in the figure, Te

reached 900 K at 114 km and 500 K at 105 km. This can be compared with 400 Kand 200 K, respectively, for the quiet period at the same altitudes. A complete setof measurements [obtained during the November 15-16 1984 EISCAT campaign]is presented as a scatter plot of the electron temperature versus altitudes in Figure14 [St.-Maurice et al., 1990]. As we move from left to right, the full lines corre-spond to the envelopes within which we can find 1%, 5%, and 95% of the meas-urements. In Figure 15, the same electron temperature data is presented for alti-tudes between 110 to 115 km as function of the electron density and of the elec-tron E x B drift, where E is the electric field, and B is the magnetic field [St.-Maurice et al., 1990].

58

Figure 14. Scatter plot of electron temperatures measured at various altitudes on the night ofNovember 15-16, 1984 with the EISCAT radar. The data cover 12 hours of measurements using1 min integration time. The curves of electron temperature versus latitude correspond to theenvelopes within which 1%, 5% and 95% of the measurements fall in moving from left to rightrespectively.

Figure 15. Electron temperature as a function of both the electron density and the magnitude ofthe E x B drift for data obtained in the 110 to 115 km altitude gates. This figure only shows theaverage behaviour of the electron temperature, and not the individual data points.

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From the observational point of view, the anomalous heating can be character-ised by the following features [St.-Maurice et al., 1990] :

[1] Te increases below 120 km when the electric field E increases. For E close to75 mV.m-1 Te is close to 1000 K at 112 km.

[2] Te peaks around 112 km.

[3] Te can be as large as 2000 K to 3000 K. This can happen about 5% of the timeduring very active conditions.

[4] the larger Te becomes, the more short-lived a heating event appears to be.

[5] Te is probably anti-correlated to the ambient electron density but is still quitevariable even after allowing for this density effect.This experimental description seems to be exhaustive but there now remains

the question : what is the heating mechanism? The studies made by Schlegel andSt.-Maurice [1981], Wickwar et al. [1981], and Robinson [1986] showed that onecan eliminate all classical processes such as electron precipitation, heat conduc-tion or classical frictional heating.

Precipitation can be eliminated because:

a) the electron temperature increases are not related to increases in the electrondensity and

b) the heating rates would have to be orders of magnitude greater than calcu-lated [Schlegel and St.-Maurice, 1981].

Heat conduction is also out of the question simply because a strong peak is ob-served in the electron temperature around 112 km, which indicates a local heatsource rather than conduction of heat from another region [Schlegel andSt.-Maurice, 1981]. The classical frictional heating mechanism looks more prom-ising since the electron temperatures are strongly correlated with the ambientelectric field. However, this mechanism suffers from a kind of deficiency which issimilar to that which is found with the other explanations : not only is the heatingrate from this source an order of magnitude too small, but it is very difficult to usethis mechanism to explain how the electron temperature would reach a peak atany particular altitude since both the heating and cooling rates are proportional tothe neutral density in the region [St.-Maurice, 1987, reply to D’Angelo and Mer-lino, 1987). Note that D’Angelo and Merlino [1987] have nevertheless proposedfrictional heating as a possibility by playing with the cooling rates of various spe-cies as a function of the altitude.

The above arguments have led people to conclude that the electrons are heatedby plasma turbulence through large amplitude plasma waves generated by the

60

Farley-Buneman and/or gradient-drift instabilities. This readily explains why theelectrons are hottest at 112 km altitude and also why no elevated electron tem-peratures are ever found in the E region when the electric field is less than20 mV.m-1 [the latter being the threshold value for the Farley-Buneman instabil-ity]. The basic theory simply uses the fact that the perturbed low frequency cur-rents generated by the large amplitude electrostatic waves give rise to additionalJoule heating. Beyond that point, two schools of thought have emerged over theyears. These differences of opinion can be traced back to two different publica-tions. First, Robinson [1986] suggested that the heating could be due to ananomalous increase in the electron Pedersen conductivity. The physical interpre-tation associated with this mechanism is that as they moved in response to the ap-plied electric field, electrons would be scattered off the perpendicular to B by theperpendicular electric fields of large amplitude wave packets. The resulting in-crease in the diffusion coefficient would not only increase the particle heatingrates, but also lead to a stabilisation of the instability, using a very similar valuefor the collision frequency at the wave, or perturbed, level.

While Robinson’s [1986] idea is elegant because it simultaneously explains theelectron heating rates and the fact that the large amplitude waves move at thephase velocity associated with threshold conditions, it has not gone without chal-lenge. In particular, St.-Maurice and Laher [1985] concluded that a more straight-forward way to heat the electrons was to have the waves evolve electric fieldswith a component parallel to the magnetic field. Such fields are observed, and thewave amplitudes inferred from this process seemed to be reasonable when com-pared to observations [see also the review by St.-Maurice, 1990]. Physically, forthis alternate mechanism, electrons were seen to be much more mobile along themagnetic field than perpendicular to it. The electrons can therefore suffer largeaccelerations with rather small parallel fields and be heated in the process. Theremaining question of the phase velocity was left behind with the original St.-Maurice and Laher [1985] explanation. Hamza and St.-Maurice [July 1993, firstpaper] are now proposing that in a situation for which the driving force is weaklyaffected by the instability, one should expect the non-linear phase velocities of thelargest amplitude waves to correspond to zero growth rates simply because wavesreach their largest amplitudes just before their "instantaneous growth rate" turnsnegative [the instantaneous growth rate has to be distinguished from the statisti-cal one, which has to be zero in steady state turbulence].

While the debate about the physical mechanism is still going on and is certainlyrelevant, it seems important to emphasise that there now exists a general consen-sus about the fact that the electrons are heated by the intense plasma turbulencethat takes place at E-region heights when the ambient electric fields are strong.The final resolution of the debate is now pointing to increasingly complex studies

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of the plasma turbulence. It would therefore appear that a final resolution of thewave heating debate will indeed involve fully turbulent, strongly non-linear, con-ditions. Examples of the evolution in thinking that has been taking place recentlycan be found in recent papers by Robinson [1994] and Hamza and St.-Maurice[the 2 July 1993 papers].

5. ConclusionThe purpose of this short lecture is to show the different types of waves and in-

stabilities existing in the ionospheric plasma and observable by the incoherentscatter technique. We describe the fluid and kinetic approach of waves in theplasma. The simplicity of the fluid approach and its possibility to give a nicephysical insight of the waves guided us in using this description. Only the kineticapproach gives the possibility to introduce the Landau damping concept. Thereare many text books studying wave phenomena in plasma and this is why we arerelatively concise in our lecture. The discussion of the observations is more de-veloped. The physical and geophysical mechanisms responsible for the observa-tions are indicated and analysed.

For people interested in the subject, we indicate here below an exhaustive bib-liography.

6. References :Barakat A. R. and D. Hubert, Comparison of Monte Carlo simulations and

polynomial expansions of auroral non-Maxwellian distributions. Part 2 : The 1-D representation, Annales Geophysicae, 8, 697-704, 1990.

Barakat A. R, R. W. Schunk and J. P. St.-Maurice, Monte Carlo calculations ofthe O+ velocity distribution in the auroral ionosphere, J. Geophys. Res., 88,3237-3241, 1983.

Cabrit B., H. Opgenoorth and W. Kofman, Comparison between EISCAT UHFand VHF back-scattering cross-section submitted to J. Geophys. Res., 101,2369-2376, 1996.

Chen F., Introduction to Plasma Physics and Controlled Fusion, Volume 1:Plasma Physics, Plenum Press, second edition, 1984.

Collis, P. N., I. Haggström, K. Kaila and M. T. Rietveld, EISCAT radar obser-vations of enhanced incoherent scatter spectra; Their relation to red aurora andfield-aligned currents. Geophys. Res. Lett., 18, 1031-1034, 1991.

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D’Angelo and R. L. Merlino, Are observed broadband plasma wave amplitudeslarge enough to explain the enhanced electron temperatures of high latitude E-region by St.-Maurice and Laher. J. Geophys. Res. , 92, 321-323, 1987.

Dougherty J. P. and D. T. Farley, A theory of collision dominated electron den-sity fluctuations in a plasma with applications to incoherent scattering. J. Geo-phys. Res., 68,5437-5486, 1963.

Evans J. V., Theory and Practice of Ionosphere Study by Thomson Scatter Radar,Proceedings of the IEEE, vol. 57,No 4, 1969.

Forme. F. R. E., A new interpretation on the origine of enhanced ion acousticfluctuations. Geophys. Res. Lett., 21, 1994.

Forme. F. R. E., J-E. Whalund, H. Opgenoorth, M. A. L. Persson and E. V.Mishin, Effects of current driven instabilities on the ion and electron tempera-tures in the topside ionosphere. J. Atmos. Terr. Phys., 55, 647-666, 1993.

Foster. J. C., C. del Pozo and K. Groves, Radar observations of the onset of cur-rent instabilities in the topside ionosphere. Geophys. Res. Lett., 15, 160 -163,1988.

Gaimard P., C. Lathuillere and D. Hubert, Non-Maxwellian studies in the auro-ral F region : a new analysis of incoherent scatter spectra, J. Atmos. Terr. Phys,58, 415-433, 1996.

Hagfors T., Density fluctuations in a plasma in a magnetic field, with applica-tions to the ionosphere J. Geophys. Res.., 66, 1699-1712, 1961.

Hamza A. M. and J. P. St.-Maurice, A turbulent theoretical framework for thestudy of current-driven E Region irregularities at high latitudes: basic deriva-tion and application to gradient-free situations J. Geophys. Res. 55, 11587-11600, 1993.

Hamza A. M. and J. P. St.-Maurice, A self-consistent fully turbulent theory ofAuroral E region irregularities. J. Geophys. Res. 55, 11601-11614, 1993.

Hubert D., Auroral ion velocity distribution function : generalized polynomialsolution of Boltzmannn’s equation, Planet. Space Sci., 31, 119-127, 1983.

Hubert D., Non-Maxwellian velocity distribution functions and incoherent scat-tering of radar waves in the auroral ionosphere, J. Atmos. Terr. Phys., 46, 601-611, 1984.

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Hubert D. and A. R. Barakat, Comparison of Monte Carlo simulations andpolynomial expansions of auroral non-Maxwellian distributions. Part 1 : The 3-D representation, Annales Geophysicae, 8, 687-696, 1990.

Hubert D. and C. Lathuillere, Incoherent scattering of radar waves in the auroralionosphere in the presence of the high electric fields and measurements prob-lems with the EISCAT facility. J. Geophys. Res. ., 84, 3653-3662, 1989.

Ishimaru S., Basic Principles of Plasma Physics - A statistical approach, A lec-ture note and reprint series, 1973.

Igarashi and K. Schlegel, Electron temperature enhancements in the polar E-region measured with Eiscat, J. Atmos. Terr. Phys., 49, 273-280, 1987.

Kikuchi K., J. P. St.-Maurice and A. Barakat, Monte Carlo computations of F-region incoherent radar spectra at high latitudes and the use of a simple methodfor non-Maxwellian spectral calculations., Annales Geophysicae, 7, 183-194,1989

Kindel J. M and C. F. Kennel, Topside current instabilities, J. Geophys. Res..,76, 3051, 1971.

Kofman W., The F and E region studies by incoherent scatter radar Adv. Space.Res. 9,5, 7-17, 1989.

Kofman W, C. Lathuillere and B. Pibaret, Neutral atmosphere studies in thealtitude range 90 110 km using Eiscat, J. Atmos. Terr. Phys., 48, 837-847,1986.

Lathuillere C. and D. Hubert, Ion composition and ion temperature anisotropy inperiods of high electric fields from incoherent scatter observations, AnnalesGeophysicae, 7, 285-296, 1989.

Lathuillere C., D. Hubert, C. La Hoz and W. Kofman, Evidence of anisotropictemperatures of molecular ions in the auroral ionosphere, Geophys. Res. Lett.,18, 163-166, 1991.

Lockwood M., B. J. I. Bromage and R. B. Morne, Non Maxwellian ion velocitydistributions observed using Eiscat, Geophys. Res. Lett., 14, 111-114, 1986.

Loranc M. and J. P. St.-Maurice, A time-dependent gyro-kinetic model of ther-mal ion upflows in the high-latitude F region, J. Geophys. Res..,99, 17429-17452, 1994.

Moorcroft D. R. and K. Schlegel, Evidence for non-Maxwellian ion velocitydistributions in the F-region, J. Atmos. Terr. Phys., 50, 455-465, 1988.

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Perault. S, N. Bjornä, A. Brekke, M. Baron, W. Kofman, C. Lathuillere andG. Lejeune, Experimental evidence of non-isotropic temperature distributionsof ions observed by EISCAT in the auroral F-region. Geophys. Res. Lett., 11,519-522, 1984.

Raman R. S. V., J. P. St.-Maurice and R. S. B. Ong, Incoherent scattering ofradar waves in the auroral ionosphere, J. Geophys. Res. 86, 4751-4762, 1981.

Rietveld M. T., P. N. Collis and J. P. St.-Maurice, Naturally enhanced ionacoustic waves in the auroral ionosphere observed with the EISCAT 933-MHzradar. J. Geophys. Res. 96, 19291-19305, 1991.

Robinson T. R., Towards a self-consistent non-linear theory radar auroral back-scatter, J. Atmos. Terr. Phys., 48, 417-422, 1986.

Robinson T. R., The role of natural E-region plasma turbulence in the enhancedabsorption of HF radio waves in the auroral ionosphere : implications for RFheating of the auroral electrojet. Annales Geophysicae, 12, 316-332, 1994.

Salpeter E. E., Plasma density fluctuations in a Magnetic field, The PhysicalRev., 122, 6, 1663-1674, 1961.

Schlegel K., and J. P. St.-Maurice, Anomalous heating of the polar E-region byunstable plasma waves. J. Geophys. Res., 86, 1447-1452, 1981.

St.-Maurice J. P., Reply J. Geophys. Res. , 92, 323-327, 1987.

St.-Maurice J. P., Electron heating by plasma waves in the high latitude E regionand related effects : Theory, Adv. Space. Res. 10,6,239-249, 1990.

St.-Maurice. J. P. and R. Laher, Are observed broadband plasma wave ampli-tudes large enough to explain the enhanced electron temperatures of the highlatitude E-region? J. Geophys. Res. , 90, 2843-2850, 1985.

St.-Maurice J. P. and R. W. Schunk, Auroral ion velocity distributions for a po-larization collision model, Planet. Space Sci., 25, 243-260, 1977.

St.-Maurice J. P. and R. W. Schunk, Ion velocity distributions in the high lati-tude ionosphere. Rev. Geophys. Space Phys., 17, 99-134, 1979.

St.-Maurice J. P. and R. W. Schunk, Ion neutral momentum coupling near dis-cret high-latitude ionospheric features, J. Geophys. Res.., 86, 13, 11299-11321,1981.

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St.-Maurice J. P.,W. B. Hanson and J. C. G. Walker, Retarding potential ana-lyser measurements of the effect of ion-neutral collisions on the ion velocitydistribution in the auroral ionosphere, J. Geophys. Res. ., 81, 5436-5446, 1976.

St.-Maurice J. P., W. Kofman and E. Kluzek, Electron heating by plasma wavesin the high latitude E region and related effects : Observations, Adv. Space. Res.10, 6, 225-237, 1990.

St.-Maurice J. P., W. Kofman and D. James, In situ generation of intense par-allel electric fields in the lower ionosphere, J. Geophys. Res., 101, 335-356,1996.

Suvanto K., M. Lockwood, K. J. Winser, A. Farmer and B. J. I. Bromage,Analysis of incoherent scatter radar data from non-thermal F-region plasma, J.Atmos. Terr. Phys., 51, 483-495, 1989.

Whalund J-E., F.R.E. Forme, H.J. Opgenoorth, M.A.L. Persson, E.V. Mishinand A.S. Volkitin, Scattering of electromagnetic waves from a plasma: en-hanced ion acoustic fluctuations due to ion-ion two stream instabilities. Geo-phys. Res. Lett., 19, 1919-1922, 1992.

Whalund J-E., H.J. Opgenoorth, F.R.E. Forme, M.A.L. Persson, I. Hägg-strom and J. Lilensten, Electron energization in the topside auroral ionosphere: on the importance of ion-acoustic turbulence, J. Atmos. Terr. Phys. , 55, 623-646, 1993.

Wickwar. V.B, C. Lathuillere, W. Kofman and G. Lejeune, Elevated electrontemperatures in the auroral E layer measured with the Chatanika radar. J. Geo-phys. Res. , 86, 4721-4730, 1981.

Wilson G.R., Kinetic modelling of O+ upflows resulting from ExB convectionheating in the high latitude F-region ionosphere J. Geophys. Res., 99, 17453-17466, 1994.

Winkler E., J. P. St.-Maurice and A.R. Barakat, Results from Improved MonteCarlo : Calculations of Auroral Ion Velocity Distributions, J. Geophys. Res. ,97, 8399-8423, 1992.

Winser K.J., M. Lockwood and G.O.L. Jones, Non-thermal plasma observationsusing EISCAT : aspect angle dependence, Geophys. Res. Lett., 14, 957-960,1987.

Winser K.J., M. Lockwood, G.O.L. Jones and K. Suvanto, Observation of non-thermal plasma at different aspect angles, Geophys. Res. Lett., 94, 1439-1449,1989.

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67

MODULATION OF RADIOWAVES FOR SOUNDING THEIONOSPHERE: THEORY AND APPLICATIONS

Asko Huuskonen - Markku Lehtinen

1. IntroductionModern incoherent scatter measurements rely on most complicated coding

schemes to bring statistical accuracy to the measurements.Various methods tomake use of longer transmission modulations than the required final resolutionshave been developed in order to facilitate full use of radar duty cycle and thusmake the results accurate enough for analysis. These methods include phasecoding, multipulses, phase coded multipulses, alternating codes and many othermethods and combinations of different methods [Farley, 1969, 1972; Turunenand Silén, 1984; Turunen, 1986; Lehtinen and Häggström, 1987; Sulzer, 1986,1993; Nygrén et al., 1996; Huuskonen et al., 1996; Markkanen and Nygrén,1996].

The data gathered by these methods never represent point values of the plasmaproperties in the ionosphere, but rather some averages of the plasma effectiveautocorrelation function in both the lag variable and the range variable. Thefunctions specifying the form of the averages are called weighting or ambiguityfunctions. The idea behind all coding methods is to cause the ambiguity functionshave a narrow form by choosing the phases of the transmission in a way so thatresponses from elsewhere than the peak itself completely or approximativelycancel out. In most general form, the ambiguity functions depend on both therange and the lagvariables.

The theory of ambiguity functions for pulse coding and phase coding methodswas pioneered by Woodman and Hagfors [1969], Farley [1969,1972] and Grayand Farley [1973], where the reduced ambiguity functions for the lag variable areshown. The study has been developed by Rino et al. [1974] and Huuskonen et al.[1988] to include the reduced ambiguity functions for range. A fully generalderivation of two-dimensional ambiguity functions appears in Woodman [1991].That study is not restricted to the case of incoherent scatter. It covers e.g. also thecase where plasma fluctuations may correlate over large distances. A recenttreatment is given by Lehtinen and Huuskonen [1996] which is based on Lehtinen[1986].

In this paper, we will present the most important ambiguity function formulas,based on the formalism by Lehtinen and Huuskonen [1996]. We will visualize thefunctions by using the range-time diagrams and by showing in detail how theambiguity functions are created graphically. The aim is to give sufficient

68

env(t)

p(t)

z=(p*e)

correlator

receiver

z(t)z(t')

lag profiles

t

t'

e(t)

Figure 1. A schematic description of an incoherent scatter experiment

knowledge of the ambiguity functions so that the reader is able to understand howthe most common incoherent scatter modulations, single pulses, pulse codes andalternating codes, work.

2. Ambiguity functions in practiceFigure 1 shows the equipment and processes relevant to our discussion. The

transmitter antenna transmits a radiowave, modulated by env(t) to the ionosphere.Incoherent scattering occurs in the ionosphere, and a tiny part of the transmitted

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power scatters towards the receiving antenna. In the bistatic configuration, shownin the figure, the scattering volume is formed by the geometrical intersection ofthe antenna beams. We will be mostly work with the monostatic configuration,where the receiver and transmitter antennas are in the same location. In themonostatic case a spatially narrow scattering volume is obtained by a suitablechoice of the modulation and signal processing.

The receiver antenna detects, after the signal has been transferred to zerofrequency by multiple analog [or partly digital] mixer stages, a complex voltagee(t). The voltage is filtered by the received impulse response p(t) and sampled.The samples form a sample vector, from which a set of crossed products z(t)z(t’)are calculated by the correlator device and stored.

Figure 2 introduces the standard tool, the range-time diagram, to displaymodulations and sampling. On the x-axis, the transmitter envelope is shownstarting at time instant 0. The present envelope consists of three pulses, positionedat times 0, 2 and 6 in our normalized units. The modulation is called as a 3-pulsecode. The oblique lines starting from the pulses show the locations of the pulses atlater time instant.

0 2 6 150

2

4

6

8

10

12

14

16

Transmission/sampling time

Ran

ge

Figure 2. Range-time diagram for a three-pulse experiment. The transmitter envelope is denotedby the dotted blocks and the receiver impulse response by the solid block in the horizontal axis.

At time instant 15, another box of unit length is found. This box, from which avertical line originates, shows the form and duration of the receiver impulseresponse [p in the formulae]. In our example, the impulse response is a box-car

70

of unit length, which means that the scattered signal returning from theionosphere is averaged over that time interval before being sampled.

A note on the units is needed. In figure 2, both the time and range is measuredby same units. The reception time corresponds to the total travel time from thereceiver through the scattering volume to receiver. Therefore, if we think ofmonostatic case where the transmitter and receiver are located at the same place,the true range to the scattering volume is obtained by multiplying half of the totaltravel time by the velocity of light or the total travel time by half of the velocity oflight.

The rhombic regions show the support of the amplitude ambiguity function ofthe sampled signal,

WtA(u;S) = p(t-u) env(u-S) (1) [13]

where S is the range variable, u is the time variable and t is the sampling time. Thenumbers in brackets refer to Lehtinen and Huuskonen [1996]. Graphically thesupport is formed as the intersection of the oblique regions showing the pulselocations and the vertical columns denoting the sampling intervals. As both theimpulse response and the envelope are of constant value, the amplitude ambiguityfunction is also constant within the support [and zero elsewhere].

0 2 6 15 210

2

4

6

8

10

12

14

16

18

20

Transmission/sampling time

Ran

ge

Figure 3. Amplitude ambiguity functions for sampling times 15 and 21 and ambiguity functionsfor the crossed product

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The support of the amplitude ambiguity function is formed of three separateregions, which correspond to the three transmitted pulses. In the time dimensionthey span a unit time interval determined by the length of the impulse response.In the range direction on the other hand, the total range span is two units, becausethe transmitted pulses travel upwards during the finite time interval given by thefiltering. The sampled signal is composed by all the elementary signalsoriginating within the support of the amplitude ambiguity signal. Mathematicallyit is a weighted average of the elementary signals e(u;d3x) scattered fromelementary volumes at x and received at times u:

z(t) = ⌡⌠

-∞

∞ du

⌡⌠

x

e(u;d3x) WtA(u;S(x)) (2) [12]

where S(x) shows explicitely that the range is measured by the total travel timefrom transmitter to receiver via the elementary scattering volumes x.

The final measurements are crossed products of two samples. Figure 3illustrates the case for samples taken at time instants 15 and 21. The amplitudeambiguity functions of the samples both consist of three regions. When theambiguity function for the product is caluclated, the important point to note is thatonly elementary scatters from the same altitude region correlate in the statisticalsense. The part of the signal, whose region of origin does not have its counterpartin the other sample, averages to zero statistically. It is only seen as an increase ofnoise in the measurement. In our example it is noted that the first pulse of thefirst sample and the third pulse of the seconde sample give scatter from the samealtitudes. Mathematically it is stated by the formula:

Wt,t’(τ;S)= ⌡⌠

-∞

∞ du WtA(u;S) Wt’A(u-τ;S) (3) [15]

which tells that the two-dimensional ambiguity function for the lagged product isa convolution of the amplitude ambiguity functions. At any range where thatfunction of either measurement vanishes, the two-dimensional ambiguity functionvanishes as well. In terms of Wt,t’(τ;S) the lagged product is expressed as:

72

⟨ z(t) z(t’) ⟩ / R = ⌡⌠

x

d3x

⌡⌠

-∞

∞ dτ P0(x) Wt,t’(τ;S(x)) σeff (τ;x) (4) [16]

which tells that the lagged product is a weighted average of the plasma scatteringcross section σeff(τ;x). The single electron scattering power is given by P0(x).

-40-20

020

40

440460

480500

-0.05

0

0.05

0.1

Lag [us]Range [us]

Two-dimensional range-lag ambiguity function

0 0.5 1440

460

480

500

Ran

ge [u

s]

Range amb. function

-40 -20 0 20 400

1

2

Lag [us]

Lag amb. function

Figure 4. Two-dimensional and reduced ambiguity functions for the 40 µs pulse of EISCATCP1K-experiment

From the convolution formula it is easy to see that the two-dimensionalambiguity function for our lagged product example is a pyramid, centered at range14 and time delay 6, which corresponds to the difference of the sample times. Thefunction if shown in Figure 3. The functions to the left and below show thereduced ambiguity functions for range and lag, obtained by integrating the two-dimensional function in the other variable. The lag ambiguity function, and itsFourier transform, the spectral ambiguity function, are central to the data analysis.However, we will not study them further here. The range ambiguity function, onthe other hand, appears often in the following, because it is useful in showing howthe modulations work. As a function of the basic functions, env and p, it is givenby:

Wt,t'(S) = (p * env) (t-S) (p * env) (t’- S) (5) [20]

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Figure 4 shows the two-dimensional range-lag ambiguity function and thereduced ambiguity functions for range and lag for the 40 µs power profile pulse inthe EISCAT CP1K-experiment. The filter used is a 25 kHz linear phase filter. Thefiltering effects are seen as smoothing in the range direction.

3. The lag profile principleIf in Figure 2 we step the reception time by one unit, the amplitude ambiguity

function will step by one unit in time and range, retaining its shape. If we thensample the signal at constant intervals, we will get a sample vector z(ti), i=1 ... N,where all the elements have ambiguity functions of the same shape, but which arelocated at equidistant ranges.

Similarly, if the in Figure 3 we step both reception times by one unit, orincrease the index i in the lagged product z(ti)z(ti+k) by one, we will obtain similarambiguity functions, which will be located one unit higher in range, but at thesame lag value. From a set of samples z(ti), i=1 ... N, we may calculate crossedproducts z(ti+k), i=1 ... N - k. This is the lag profile principle which is central inunderstanding IS measurements. The principle tells that the form of the ambiguityfunctions for a given measurement depends only on the difference of the samplingtimes, whereas the range of the measurement changes by one step, if the samplingtimes are stepped accordingly. One way to think is that a lag profile consists ofidentical measurements made at a set of equidistant ranges.

4. Requirements for an experimentThe basic problems and requirements in the incoherent scatter modulation

design have been summarized by Lehtinen [1986] as follows:

"The main problem in conducting incoherent scatter measurements is the factthat, as the Thomson cross section is small and the electron densities are notvery high, the signal received is weak. It is often smaller than thebackground noise from the sky and the receivers. Moreover, if the signal isreceived with the same antenna as is used for transmission, it is necessary touse small pulses instead of a continuous wave transmission, so that theresponses from different altitudes would not be mixed with each other. Thismakes the situation still worse.

There are four resolution requirements that have to be taken into account in adesign of a measurement. The first one is spatial resolution. This resolutiondetermines the basic pulse widths used. The second one is the lag resolution,by which we mean the time in which the phase and amplitude of the scatteredsignal itself does not change significantly. Thus, it is the typical

74

scale of the autocorrelation functions. The third one is the time resolution, bywhich we mean the time scale for the changes of the plasma parametersthemselves. During this length of time it is possible to reduce measurementerrors by repeating the experiment as many times as the radar duty cycles andother relevant factors allow. This is called integration, and consequently, thetime resolution is often called integration time. The last one is then therequired accuracy of the autocorrelation function estimates calculated.

In addition there are two basic extent requirements. The first one is that theexperiment produces data from a long enough altitude interval to be useful.This poses a limit to the repetition frequency of the experiment. The secondone is that the experiment must provide data over a broad enough laginterval. These intervals are called range extent and lag extent, respectively.

The requirements of having all of the resolutions accurate are contradictorywith each other when the design of the experiment is restricted withtechnical factors, such as radar peak power, radar duty cycle etc. As it isoften impossible to meet all the requirements with straightforwardtechniques, a number of different methods of coding the transmission,perhaps using a series of coded groups with different frequencies, are beingemployed to use the radar equipment as effectively as possible. Thesemethods have in common the property that they produce data with specifiedresolutions, but with better accuracy than a simple pulse or a pair of pulseswould do."

0 50 100 150 200 250 300 350-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

100

150

200

300

Lag [microseconds]

Figure 5. Plasma autocorrelation function for 931.5 Mhz. at altitudes given in the figure

Of the above requirements, the range resolution, lag resolution and lag extentsare central for the modulation design. The plasma ACF at 100, 150, 200 and 300km altitudes [for frequency 931 MHz] are shown in Figure 5, from

75

which it is possible to obtain rough estimates for the last two. The lag resolutionshould be better than the width of the ACF, as determined by the value of the firstzero crossing. The crossing occurs at 160 µs at 100 km, at 70 µs at 150 km andbelow 50 µs higher up. The lag resolution used in practice varies from 20 and 40µs in the E-region measurements and is generally below 15 µs in the F-regionmeasurements. The required lag extent puts a constraint on the modulation design,because the total modulation length must exceed the lag extent. In practice, thelongest lag measured varies from 300-350 µs in the E-region to 250 µs in the F-region, but may be shorter than that higher up. Precise numerical estimates for thesufficient lag resolution and extent are obtained by following the procedurepresented by Vallinkoski [1988]. The range resolution required is about 3 km inthe lower E-region and increases with increasing height. In the F-region, a rangeresolution of some tens of kilometers is sufficient.

The above is correct for E- and F-regions only. In the topside ionosphere,where hydrogen is important, the plasma ACF is much narrower and therefore abetter lag resolution is needed. The ion velocities can only be high there, whichstill increases the required lag resolution. In the D-region, on the other hand, theplasma ACF is much wider and the lag resolution is of the order of milliseconds.

The operating frequency also affects lag resolution and extent. At 500 Mhz,which is the operating frequency of the EISCAT Svalbard Radar, the plasma ACFis roughly twice as wide as at the EISCAT UHF-frequency, which must be takeninto account in the modulation design.

p

env

p*env

Lag 0

Lag 40

Lag 80

Lag 120

Lag 160

Lag 200

Lag 240

Sampling time/range

Figure 6. An illustration to show how the range ambiguity functions can be formed graphically.The pulse is 320 µs long and the receiver impulse response 20 µs long. The transmitter envelopeenv is shown at the bottom, filter impulse response p and p * env next and the range ambiguityfunctions at multiples of 40 µs above.

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5. Single pulse modulationThe simplest modulation of all is an uninterrrupted pulse of sufficient length.

The length of the pulse is chosen to exceed the lag extent, in order that the fulllength of the plasma autocorrelation function is measured. This kind modulationsis called single pulse or long pulse modulation.

Figure 6 illustrates how the range ambiguity functions for a single pulseexperiment can be formed graphically. We assume a transmitter envelope of 320µs long, shown at the bottom of the figure, and a receiver impulse response,which is a box of 20 µs long. According to Eq. 5 the starting point is theconvolution of the impulse response and the transmitter envelope, which is shownin the figure (p * env). The sampling interval is 20 µs and the sampling times areshown by small tics in the time axis. We will denote the sampling times by ti, i =1 ... N. In the EISCAT CP1K experiment the sampling time is 10 µs instead of 20µs.

We can see in the figure how the range ambiguity functions for even multiplesof 20 µs are created [odd multiples have been excluded to keep the figure simple].First p * env is shifted by the value of the lag in question. Then the shifted p *env is multiplied by the unshifted one. The products are shown as shaded regions,

which show the range ambiguity functions of the crossed products : z(t1)* z(t1+k)

, k=0, 2, 4 ... 12.

0 20 40 60

0

10

20

30

40

50

60

<−−

t1: s

ampl

ing

time

for

the

first

fact

or

t2: sampling time for the second factor −−>

Figure 7. A lag profile matrix and crossed products belonging to a single gated long pulsemeasurement

77

It is seen that the range ambiguity function for the zero lag is as long asp * env, but that the ambiguity functions for the longer lag values are shorter. Thismeans that the scattering volumes are of different size. This fact had twofoldconsequences. The shorter lags given an average over a larger altitude rangewhich is a disadvantage is the plasma is not sufficiently homogeneous. On theother hand they collet a bigger signal than the longer lags, which increases theaccuracy for low SNR.

The data from the present day long pulse experiments are processed so that alarger number of estimates of the longer lags are included in the final estimate.The selection procedure is illustrated in Figure 7, which shows a lag profilematrix. A lag profile matrix is formed by calculating all crossed products from themeasured sample vector and by arranging the results so that y-axis is formed bythe sample time of the first factor in the product and the x-axis by the sampletime of the second factor. The products shown in Figure 6 are located on the firsthorizontal line. Points on any diagonal have the same difference of the sampletimes, i.e. the same lag value. The main diagonal contain points, where the sampletimes are equal. If both sampling times are advanced by one sampling unit, thenext point on a lag profile is obtained.

0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5

23

ms

27

31

35

39

43

47

Figure 8. Range ambiguity functions for a gated long pulse experiment

78

When looking at the matrix elements selected for a gated long pulsemeasurement, we first notice that certain number of elements have been leftunused from the lag profiles with small lag values. This has been done becausethe first elements in the lag profiles have center points at closer ranges than thelonger lag values do. Another point to note is that more elements are included inthe averaging for longer lag values. This compensates for the smaller scatteringvolumes which the individual measurements have. One should note that, if thenext gate is formed by using the next 15 elements from the zero lag profile,certain elements in the non-zero lag profiles will be used by two consecutivegated measurements, i.e. the measurements will not be independent.The gating isdone in order to reduce the number of result memory locations neededand also toease the task of analysis programs.

The range ambiguity functions for the long pulse modulation of the EISCATCP1K-experiment are shown in Figure 8. Here the pulse length is 350 µs, filteringis done by a 50 kHz Butterworth filter, and sampling is done at 10 µs intervals.Lag estimates are calculated at 10 µs intervals up to 250 µs and 15 estimates areadded together for final gated zero lag estimate. It is seen that the functions havethe same peak-to-peak coverages although they differ in details.

Figure 8 shows that the scattering volume for a long pulse measurement is long.It is easy to understand that the volume must necessarily be longer than the pulseitself, e.g. 350 µs ≈ 52 km, and that a gated measurement has a even longervolume. This restricts the use of long pulses the the F-region, where the plasmaproperties do not change too much over such distances. Another fact is that a longpulse is the most efficient measurement in the region where it can be used.

In the above example, as well as in the practical examples, the pulse is is longerthan the lag extent would require. A longer pulse is used because the scatteredsignal is stronger, which is advantageous at the long ranges and low electrondensities. For very long ranges pulses as long as 2000 µs may be used.

6. Pulse codesThe single pulse modulation is unsuitable for E-region work, because the

scattering volume is much longer than the scale height of the plasma parametersin the E-region. The first modulation method to give adequate range resolution inthe E-region work was the pulse code [multiple-pulse, multi-pulse] method,pioneered by Farley [1972] and Rino et al. [1974]. The technique was developedinto its full power when the interlaced multi-pulse codes [Turunen and Silén,1984, Turunen, 1986] came into use with the EISCAT UHF-radar. The interlacedcodes are based on the ability of the EISCAT transmitters to change frequencyrapidly so that gaps are not left in the transmission and the full radar duty cyclecan be used efficiently.

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A classical pulse code modulation fullfils the following conditions:[1] Code consists of N pulses of equal duration.[2] The distance of any pair of pulses is an integer multiple of the smallest

interpulse distance and all distances are different. The smallest distance givesthe lag resolution of the code.

[3] The sum of the pulse length and receiver impulse response is less than thesmallest distance of pulses.

Fullfilment of these conditions quarantees that all non-zero lags will haveambiguity functions of same size and shape and that the scattering volume isuniform, i.e. not formed by two or more separate volumes. This is illustrated byFigure 9, which shows how the range ambiguity functions for a 4-pulse code areformed. As in Figure 6, the calculation proceeds so that first p * env is calculated,assuming that p is in form similar to any of the pulses of the code, and then p *env is shifted by the lag value in question and the two functions are multiplied.The key point is the fact that only signals from the same altitude correlate witheach other. At any non-zero lag, only one triangle in the p * env of the firstsample coincide with the p * env of the second sample. Therefore only onealtitude range produces a statistically meaningful average, the signal productsfrom the other ranges only show up as noise which averages to zero. Theexception is the zeroth lag, which gets contribution from four separate ranges.

env

p*env

Lag 0

Lag 1

Lag 2

Lag 3

Lag 4

Lag 5

Lag 6

Figure 9. A 4-pulse code and how the range ambiguity functions are formed. The impulseresponse function is box-car shaped.

The six lag values in Figure 9 correspond to the time differences of the leadingedges of the transmitted pulses. A 4-pulse code gives well behaving estimates atsix different lag values, which correspond to the six different pulse pairs obtainedfrom the code. In this sense we can thing a four pulse code as formed by fourvirtual two pulse codes, each giving measurements at one lag value. A multipulsecode is more efficient that multiple two pulse codes would be. Four pulses are

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sufficient to produce estimates at six different lag values, whereas six separatetwo- pulse measurements would require 12 pulses altogether for the same effect.

The range ambiguity function in Figure 9 are also similar to those of a singlepulse of the length of the individual pulses in the pulse code. Such pulses are usedto measure the zeroth lag estimates for the multipulse autocorrelation functions.The optimal use of the multipulse data requires that the zeroth lag of themultipulse is also used. Although any measurement is a sum of contributions frommultiple altitudes, it is possible to use the data [Lehtinen and Huuskonen, 1986].

Any other lag value than those corresponding to pulse separations will lead toambiguity functions which are of different shape and, in most cases, includeseveral separate regions. An example is shown in Figure~5 of Lehtinen andHuuskonen [1996].

The design principles of the pulse codes put restrictions on the number possiblepulse codes. The smallest pulse separation must be twice the basic pulse length toallow space for the receiver impulse response. Therefore the lag resolution will beat least twice the basic pulse length.In the case of the EISCAT UHF radar thefollowing combinations have turned out to be the most practical ones:

Number of pulse smallest distance code lagpulses length lag resolution sequence values

4 20 40 [1 3 2] 1 ... 65 14 30 [ 2 5 1 3] 1 ... 9, 11

0 30 60 90 120 150 180 210 240 270 300 330 360 390

Figure 10. An interlaced 5-pulse code set used in EISCAT CP1H experiment.

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The code sequence gives the pulse locations in units of the smallest distance[lag resolution]. The choice of the pulse lengths is constrained very much by theconditions required from pulse code. For instance,

[1] - The longest lag obtained from the 4-pulse code is only 240 µs long, which isnot sufficient for all E-region conditions. Longer lags could be obtained bychanging the lag resolution from 40 µs to 50 µs, but this would limit the use ofthe code to the lower E-region only, where the plasma ACF is wide.

[2] - The 14 µs pulse used in the 5-pulse code gives lower power than the 20 µspulse use in the 4-pulse code. A longer pulse length would be optimal, but isnot possible, as the total duration of the modulation would exceed the allowedlimits.The unavoidable gaps in the pulse codes lead to loss of radar duty cycle. The

EISCAT radars are able to interlace many codes at different frequencies into thesame transmission, and then only 1 µs is lost at every frequency change. Anexample is shown in Figure 10. Interlacing increases the number of independentlag estimates obtained. The 5-pulse codes in the figure use altogether26 (x 15 µs ) units of transmission time. Each code uses 5 units and gives 10independent lag estimates [we neglect the zero lag, which is ambiguous], so thatthe 4 codes give 40 estimates. It is usual to include some power profile pulses inthe transmission as well. The power values are then used as zero lags in theplasma autocorrelation function. The multipulse zero lags are mostly discarded asthey represent sums of powers from many altitudes.

Figure 11. A 4-bit alternating code set (above) and p * env for the codes (below)

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7. Alternating codesAlternating codes [Lehtinen and Häggström, 1987] are the state-of-the-art

modulation method for the E-region and lower F-region measurements and theyhave replace multipulse codes in most applications. An alternating code is anuninterrupted transmitter pulse, which consists of N parts, called bits or bauds,each having either positive or negative phase [All pulses in a multipulse havesame phase]. If a sufficient number of these pulses, all different, are usedtogether, it is possible to get measurement with a height resolution correspondingto the bit length, and not to the total pulse length. It is somewhat difficult to findthese code sets, but once the set is available, it is fortunately much easier tounderstand how the code set works. In general, a N-code set consists of 2 Ncodes, if N is a power of two. For other values we have to take twice the power oftwo which is larger than N. Lehtinen and Häggström [1987] gave codes up tolengths of 32 bits but recently an efficient method to find much longer codeshave been developed [Markkanen and Nygrén, 1996].

To understand how alternating codes work we study 4-bit code set consisting of8 codes in the upper panel of Figure 11. The bottom panel shows how p * envlooks like for the codes, if the filter impulse response is as long as one bit in thecode. Figure 12 shows how the range ambiguity functions for a lag [equal to bitseparation] look like for each of the 8 individual codes. It is found that they allcover a altitude region which is four bits long, i.e. one bit less than the altitudespan of p * env On the right one can see three decoded measurements whosepeak-to-peak coverage is only 2 bits long, i.e. the range ambiguity functions areidentical to those from a power profile pulse measurement with pulse length ofone bit.

The decoding coefficient are obtained from the signs of the bauds which for the8 codes in question are:

Bit 1 2 3 4 5 6 7 8 Code1 + + + - - - - +2 + - - + + - - +3 - + - + - + - +4 + + + + + + + +

Comparison of the signs and Figure 11 shows that the signs tell whether aaltitude region gives a positive or negative contribution to the signal. Thedecoding signs for a lag estimate are obtained if delay the signs by one step andmultiply them with the original. A comparison with Figure 12 shows indeed thatthe signs in the following table:

83

Prod 1 2 3 4 5 6 7 8 Code(1,2) + - - - - + + +(2,3) - - + + - - + +(3,4) - + - + - + - +

agree with the positively and negatively contributing regions in the individualrange ambiguity functions. When each range ambiguity function is multiplied bythe corresponding sign in the first row, the contibution from the upmost range willalways be positive, but there will be equally many positive and negativecontributions from ranges 2 and 3, which will cancel out precisely. This wouldnot happen for a randomly chosen sign set, but is a result of the fact that the codesform an alternating code set. A similar cancellation of unwanted contributionshappens for the second or third range, if the signs in the corresponding row areused. For the second lag one gets two estimates, for the two upmost ranges.Finally it is possible to one estimate for the third lag.

Figure 12 shows that we can treat an alternating code as a set of co-existingtwo-pulse experiments. The upmost decoded range ambiguity function would beobtained from an experiment containing the first two bits of the modulation only.The second ambiguity function would come the two next bit etc. In general, a N-bit alternating code corresponds to N * (N-1) / 2 simultaneous two-pulseexperiments.

Figure 12. Range ambiguity functions for individual codes and for the decoded measurement

The great advantage of alternating codes is that the transmitter modulation timeis used efficiently. This is seen by calculating the number of independentestimates obtained. Figure 10 shows that it is possible to fill in the transmissiontime by interlaces multipulses and power profile pulses. If the gaps in thetransmission are filled by power profile pulses, altogether 46 independent

84

estimates are obtained. When all the transmission is on a single frequency, we willget altogether 26 * 25 / 2 = 325 pulse pairs, all giving one estimate, which isabout 7 times that from the multipulse experiment.

If the signal-to-noise ratio is high, the situation is more complex, and a pulsecode experiment may be more efficient in certain cases. Then, however, bothmodulations are able to measure the plasma autocorrelation function efficiently. Itis fair to say that alternating codes produce a balanced performance, wheresuperior accuracy at low signal levels is accompanied by a good accuracy at highsignal levels. A thorough comparison is presented by Huuskonen and Lehtinen[1996].

Another advantage is that the bit length and the total pulse length are notrelated as in the case of multipulses, where only a couple of practical solutionsexist. Let us assume that we wish to measure the autocorrelation function up tolag 320 µs, and that we wish to have a range ambiguity function similar to that ofa 20 µs pulse. This means that the range resolution wanted is 16 times better thanthe total pulse length we have to use. This is possible by taking a 16-bit [or 16-baud] alternating code set into use. The lag and range resolutions will be equal.Alternating codes as well as multipulses are useful in the region where the rangeresolution needed is much better than the lag extent [longer lag to measure]. Thisis true in the E-region and lower part of F-region.

Note that the zero lag is not obtained from the alternating code with the goodaltitude resolution. In the zero lag estimate all range give a positive contributionand it is not possible to make the contributions from all but one range to cancelout. This is identical to what happened to the multipulse zero lag.

The present standard EISCAT experiment use alternating codes. The CP-1-Kexperiment [Wannberg, 1993] uses 16-baud codes with a 21 µs baud length. Thefuture alternating code experiments, e.g. those planned for the EISCAT SvalbardRadar, will use oversampling and fractional lag production to improve theaccuracy and speed of the experiments still [Huuskonen et al.., 1996].

8. Other coding techniquesMultipulses, alternating codes and long pulses cover most of the applications in

incoherent scatter measurements. There are some special cases for which othertypes of codes, or combinations of the above, are needed.

If the required range resolution is very fine, e.g. 300 m in the E-region in thecase of thin metal ion layers, the individual pulses in a pulse code or analternating code are coded with a 13-bit Barker-code [Gray and Farley, 1973].Examples of using Barker-codes pulse codes are found in Turunen et al. [1988]

85

and Huuskonen [1989]. Wannberg [1993] introduced the first Barker-codedalternating code experiment. These experiments combine a very fine altituderesolution with the typical E-region lag resolution. Any Barker-coded modulation,and especially those based on pulse codes, produce tiny ambiguities to thescattering volume. The main contribution comes from a sharply defined smallaltitude region, but there are minor unwanted contributions originating fromelsewhere.

Also random codes [Sulzer, 1986] are a way of obtaining a very good rangeresolution. Random codes are coded long pulses, very much like alternatingcodes, which do not have the property of exact cancellation of the ambiguouscontributions. The cancellation happens in a statistical sense after a sufficientnumber of different codes have been transmitted and processed. A high rangeresolution is also obtained by coding individual pulses in a pulse code byalternating codes [Nygrén et al., 1996]. Now that a method of finding very longalternating codes is found, most efficient ambiguity free experiments are alsoavailable for high range resolutions [Markkanen and Nygrén, 1996].

Pulse-to-pulse experiments are used when the scattering volume is so close thatthe round trip time to the volume is shorter than the lag extent required. In the D-region case, the lag extent is of the order of 10 milliseconds, and the round triptime about 500 µs. Therefore the experiment is done so that reception happensafter each pulse, about 100 µs in duration, and crossed products are calculatedwith the samples obtained from the subsequent pulses. The individual pulses arenormally Barker-coded. The pulse-to-pulse EISCAT CP-6 experiment is explainedby Turunen [1986] and the data analysis problems by Pollari et al. [1989].

9. ReferencesFarley D.T., Incoherent scatter correlation function measurements, Radio Sci., 4,

935-953, 1969.

Farley D.T., Multiple-pulse incoherent-scatter correlation functionmeasurements, Radio Sci., 7, 661-666, 1972.

Gray R.W. and D.T. Farley, Theory of incoherent-scatter measurements usingcompressed pulses, Radio Sci., 8, 123-131, 1973.

Huuskonen A., High resolution observations of the collision frequency andtemperatures with the EISCAT UHF radar, Planet. Space Sci., 37, 211-221,1989.

Huuskonen A. and M.S. Lehtinen, The accuracy of incoherent scatterexperiments: Error estimates valid for high signal levels, J. Atmos. Terr. Phys.,58, 453-463, 1996.

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Huuskonen A., M.S. Lehtinen and J. Pirttilä, Fractional lags in alternatingcodes: improving incoherent scatter measurements by using lag estimates atnon-integer multiples of baud length, Radio Sci., in press, 1996

Huuskonen A., P. Pollari, T. Nygrén and M. Lehtinen, Range ambiguity effectsin Barker-coded multipulse experiments with incoherent scatter radars, J.Atmos. Terr. Phys., 50, 265-276, 1988.

Lehtinen M., Statistical theory of incoherent scatter radar measurements, Ph.D.thesis, 97 pp, Univ. of Helsinki, Helsinki, Finland, EISCAT Technical Note,86/45, EISCAT Scientific Association, Kiruna, Sweden, 1986.

Lehtinen M., On optimization of incoherent scatter measurements, Adv. SpaceRes., 9(5), 133-(5), 1989.

Lehtinen M.S. and I. Häggström, A new modulation principle for incoherentscatter measurements, Radio Sci., 22, 625-634, 1987.

Lehtinen M.S. and A. Huuskonen, The use of multipulse zero lag data toimprove incoherent scatter radar power profile accuracy, J. Atmos. Terr. Phys.,48, 787-793, 1986.

Lehtinen M.S. and A. Huuskonen, General incoherent scatter analysis andGUISDAP, J. Atmos. Terr. Phys., 58, 435-452, 1996.

Lehtinen M.S., L. Päivärinta and E. Somersalo, Linear inverse problems forgeneralized random variables, Inverse Problems, 5, 599-612, 1989.

Markkanen M. and T. Nygrén, A 64-bit strong alternating code discovered,Radio Sci., in press, 1996.

Nygrén T., A. Huuskonen and P. Pollari, Alternating-coded multipulse codesfor incoherent scatter experiments, J. Atmos. Terr. Phys., in press, 1996.

Pollari P., A. Huuskonen, E. Turunen and T.Turunen, Range ambiguity effectsin a phase coded D-region incoherent scatter radar experiment, J. Atmos. Terr.Phys., 51, 937-945, 1989.

Rino C.L., M.J. Baron, G.H. Burch and O. de la Beaujardière, A multipulsecorrelator design for Incoherent scatter radar, Radio Sci., 9, 1117-1127, 1974.

Sulzer M.P., A radar technique for high range resolution incoherent scatterautocorrelation function measurements utilizing the full power of klystronradars, Radio Sci., 21, 1033-1040, 1986.

87

Sulzer M.P., A new type of alternating code for incoherent scatter measurements,Radio Sci., 28, 995-1001, 1993.

Turunen T., GEN-SYSTEM - a new experimental philosophy for EISCAT radar,J. Atmos. Terr. Phys., 48, 777-785, 1986.

Turunen T. and J. Silen, Modulation patterns for the EISCAT incoherent scatterradar, J. Atmos. Terr. Phys., 46, 593-599, 1984.

Turunen T., T. Nygrén, A. Huuskonen and L. Jalonen, Incoherent scatterstudies of sporadic E using 300m resolution, J. Atmos. Terr. Phys., 50, 277-287, 1988.

Vallinkoski M., Statistics of incoherent scatter multiparameter fits, J. Atmos.Terr. Phys., 50, 839-851, 1988.

Vallinkoski M., Error Analysis of incoherent scatter measurements, Ph.D. thesis,84+26 pp, Univ. of Helsinki, Helsinki, Finland, EISCAT Technical Note, 89/49,EISCAT Scientific Association, Kiruna, Sweden, 1989.

Wannberg G., The G2-system and general purpose alternating code experimentsfor EISCAT, J. Atmos. Terr. Phys., 55, 543-557, 1993.

Woodman R.F., A general statistical instrument theory of atmospheric andionospheric radars, J. Geophys. Res., 96, 7911-7928, 1991.

Woodman R.F. and T. Hagfors, Methods for the measurement of verticalionospheric motions near the magnetic equator by incoherent scattering, J.Geophys. Res., 74, 1205-1212, 1969.

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89

THE USE OF INCOHERENT SCATTER DATA INIONOSPHERIC AND PLASMA RESEARCH

Kristian Schlegel

1. IntroductionThe incoherent scatter [IS] technique provides simultaneously several parame-

ters of the ionospheric plasma in a height range from about 90 to more than 1000km and a time resolution of the order of minutes. Four of these parameters, theelectron density ne, the electron and ion temperatures Te and Ti, and the ion drift[line-of-sight] V can generally be derived routinely. They will be called "basic"parameters in the following. Besides, the ion-neutral collision frequency can beobtained in case of sufficiently good signal-to-noise ratio [SNR] for altitudes be-low about 110 km [e.g. Kirkwood, 1986]. The relative abundance of ions withmass 16 AMU [O+] and mass 30 AMU [NO+, O2+] can be estimated in the 150-250 km height range with sophisticated techniques [e.g. Lathuillere et al., 1986]and also the abundance of H+ ions above 500 km [e.g. Wu and Taieb, 1993].

In the following chapters several techniques are described how the basic pa-rameters can be used to study various phenomena of the ionosphere and thermo-sphere. The paper should not be regarded as a thorough review article. The aimwas to give basic informations about various techniques, to present typical exam-ples, and to provide some useful references for further studies. Emphasize wasplaced on EISCAT related papers for the latter. The chosen subjects reflect somepersonal preference and do certainly not constitute a complete set. In additionthey are restricted to E- and F-region heights, since D-region and mesospheric ISapplications will be covered in a separate paper.

It is assumed that the reader has some knowledge about the principles and op-eration of an IS-system in general and about the basics of ionospheric and ther-mospheric physics [e.g. Kelley, 1989, Hargreaves, 1992].

2. Electric FieldsIn order to derive an electric field vector from IS-data one needs in general

three or more independent line-of-sight velocity estimates. These can be obtainedby looking in the same scattering volume with three different receiving antennas[Figure 1, upper left] Such a radar, like EISCAT, is called a tri-static radar. If onlyone receiving antenna is available, as in the case of a mono-static radar, the inde-pendent velocity components can be obtained by looking subsequently into threedifferent scattering volumes which are not too much separated in distance [Figure1, upper right]. It is usually accomplished by tilting the antenna beam by

90

about ±10° with respect to the original direction. In this case one has to assumethat the velocity vector is spatially constant over the distance of the respectivescattering volumes and that it is temporally constant during the measuring intervalconsisting of three separate measurements. This may not always be true duringstrongly disturbed conditions.

In both cases the three measured velocity components will then be combined inorder to obtain the velocity vector:

V = T

V1

V2

V3

(1)

Figure 1. Measurements of the ion drift velocity vector with a tri-static(upper left) and a mo-nostatic radar (upper right). Line-of-sight ion drift from Tromsoe, Kiruna and Sodankylae andthe derived electric field for a one day EISCAT experiment.

91

T is a transformation matrix the elements of which depend on the measuring ge-ometry. For further use it is convenient to express the vector V in a plane perpen-dicular to the geomagnetic field B. In this case the transformation matrix alsocontains the magnetic field orientation [Murdin, 1979].

The electric field can finally be obtained from a simplified ion momentumequation [e.g. Schunk, 1975]

νin

Ωi (V - U) = E + V x B (2)

In the F-region the ions are decoupled from the neutrals [ν in « Ωi] and there-fore Eq. 2 reduces to

E = - V x B (3)

If V is expressed in a plane perpendicular to B then Eq. 2 decomposes into:

Ex = Vy B , Ey = - Vx B (4)

where B has to be taken from a magnetic field model [e.g. IGRF 90]. Here and inthe following a coordinate system is used where the x-axis points to the east, they-axis to the north and the z-axis upward, i.e. antiparallel to the magnetic field B.In case of EISCAT the tri-static point is usually taken at an altitude of 285 km.

In the lower panel of Figure 1 the line-of-sight velocities measured during a 24hour experiment are displayed together with the derived electric field componentsperpendicular to B [Enorth = solid line, Eeast = dotted line]. It was a disturbedperiod [kp up to 8+] and therefore the electric fields reach quite high values. The maxima of the field in the afternoon and in the early morning and the turning ofthe field around 19-20 UT are quite typical for disturbed conditions. This behav-ior can be explained from the general pattern of the magnetospheric convection[e.g. Senior et al., 1990, Fontaine et al., 1986].

3. E-region electrodynamicsDue to the influence of the geomagnetic field the ionospheric conductivity is a

tensor. It can be written as [Bostrøm, 1973]

=

σP σH 0

-σH σP 0 0 0 σ||

(5)

92

Figure 2. Upper panel: Height profiles of the components of the conductivity tensor in the io-nosphere. Lower panels: Height-integrated Hall (H) and Pedersen (P) conductivities and

conductivity ratio versus time.

93

Its components are the Pedersen conductivity

σP =

νen Ωe

ν2en + Ωe +

νin Ωi

ν2in + Ωi

eB ne (6)

the Hall conductivity

σH =

Ω2e

ν2en + Ωe -

Ω2i

ν2in + Ωi

eB ne (7)

and the conductivity parallel to the geomagnetic field

σ|| =

1

me νen +

1mi νin

e2 ne (8)

Here νe, νin are the electron- and ion-neutral collision frequencies, Ωe and Ωithe respective gyro frequencies and e is the electron charge.

The collision frequencies depend on the neutral density [e.g. Kelley, 1989],which has to be taken from a model [e.g. MSIS 86], the gyro frequencies can becomputed from the local magnetic field induction B. Thus from the incoherentscatter parameters just the electron density ne is needed to calculate the conduc-tivities. It should be stressed however, that for these calculations density profilesof high range resolution [∆h ≈ a few km] are necessary which are usually providedby coded pulses.

Figure 2 [upper panel] shows an example. Since both the electron density andthe collision frequencies are strongly height-dependent, the conductivities varyconsiderably with altitude. The maximum of the Hall conductivity is usually be-tween 90 and 110 km, the maximum of the Pedersen conductivity between 120and 130 km. The latter is also important at greater heights [F-region], whereas theHall conductivity decreases strongly with altitude and is negligible above 200 km.The parallel conductivity is generally many orders of magnitude larger than theother two components because of the high mobility of the electrons parallel to B.The field lines can therefore be regarded as equipotential lines in the ionosphere.

Particularly for studies of ionosphere-magnetosphere coupling the height-integrated conductivities or conductances are important quantities. They are de-fined as:

ΣH = ⌡⌠

ho

h1 σH (h) dh ΣP =

⌡⌠

ho

h1 σP (h) dh (9)

94

Figure 3. Upper panel: Height profiles of the northward and eastward components of the currentdensity. Lower panels:Height-integrated currents and simultaneously measured magnetic fieldvariations on the ground.

For the lower value of the height integral ho usually a value between 80 and 90km is taken, h1 should be above 200 km.

Figure 2 [middle panel] shows ΣH and ΣP over a 30 hour interval. The bursts ofenhanced conductance are caused by periodic particle precipitation which causeabrupt electron density enhancement in the E-region. An important quantity is theratio of the conductances ΣH/ΣP [Figure 2 lower panel]. It is around unity duringday-time and precipitation-free conditions and increases during precipitationevents. Its value is regarded as a rough indicator of the energy of the pre-

95

cipitating particles. A recent review on high latitude conductances has been pub-lished by Brekke and Moen [1993].

As a next step in quantitative estimates of E-region electrodynamics, the cur-rent density can be computed from the equation [Ohm’s law]

J = E (10)

using the electric fields obtained as described in section 2.

If the coordinate system described in section 2 is used then this equation de-composes into the components:

jP = P E Pedersen current (⊥ B, // E)

jH = H B × E B Hall current (⊥ B, ⊥ E)

j// = // E// parallel current

(11)

It should be noted that the parallel current cannot be directly calculated fromIS-data since E// is generally too small to be measured. An estimate of j// may beobtained from:

div ( j ) = 0 (12)

stating that the total current in the ionosphere is source free. This however needs amulti point measurement in order to derive the gradients of j.

For the sake of completeness it should be noted that the electric field in eqs. 10,11 in the general case is the effective electric field

Eeff = E + U x B (13)

which accounts for a neutral wind U [see section 5].

Figure 3 [upper panel] shows an example of the current density as a function ofaltitude computed from Eq. 10. The large westward current is a consequence ofthe strong eastward flow typical for the disturbed morning hours. The smallernorthward current changes its sign due to the fact that the Hall and the Pedersenconductivity maximize at different height. Note that the westward current is not apure Hall current but has a small Pedersen contribution because the electric fieldis not a purely northward field but has also a small westward component at thattime [see Figure 1].

96

Figure 4. Upper panel:Height profiles of the Joule heating rate (qJ) and the heating rate of

precipitating particles (qP).Lower panel: Height-integrated Joule and particle heating rates

versus time.

For time series of the current variation one again uses height-integrated valuescomputed analogous to Eq. 9. Figure 3 [lower panel] shows an example for a 24-hour experiment [Araki et al., 1989]. In this figure the response of a ground-basedmagnetometer to this current is also plotted. It is obvious that both curves are verywell correlated. For a quantitative comparison, however, it has to be taken intoaccount that the ionospheric current is not a line current and that a ground-basedmagnetometer picks up contributions from a large spatial volume. Suitable as-sumptions have therefore to be made for the latitudinal distribution of the current[Lühr et al., 1994].

97

4. Heat sources and precipitationThere are several sources of energy input into the ionosphere, particularly act-

ing at high latitudes. The ohmic losses of the E-region current produce an ion andelectron heating [energy density] given by:

qJ = σP | E⊥ |2 (14)

Since this heating arises from the friction between the ions [electrons] and theneutrals it is also called frictional or Joule heating.

Both parameters in Eq. 14 can be derived from IS-data and therefore the com-putation of qJ is straightforward; Figure 4 [upper panel] shows an example.

Since σP is not negligible at F-region heights as already mentioned, Jouleheating is also very important above the E-layer current region [e.g. Baron andWand, 1983].

Another heat source provide the energetic electrons which precipitate into theE-region. The production of each electron-ion pair needs an energy of η = 35 eV.The energy density deposited in the precipitation region is therefore to a first or-der approximation [Wickwar et al., 1975]:

qP = 12 η αeff ne2 (15)

where αeff is the effective electron-neutral recombination rate [e.g. Schlegel,1985]. A profile of this particle heating during a strong precipitation event is alsodisplayed in Figure 4 [upper panel]. This heat source is practically unimportant ifno precipitation is present, e.g. during quiet conditions. This can be inferred fromthe lower panel of Figure 4 where both heating rates are plotted in a height-integrated form [analogous to Eq. 9] over an interval of 24 hours. ComparingFigure 4 with Figs. 1 and Figure 2 shows that the height integrated Joule heatingmaximizes during times when the electric field is elevated [13:00-15:00 UT] andthe particle heating during precipitation events when ne is increased. Particleheating is, however, generally smaller than Joule heating. A survey of high lati-tude heating rates has been presented by Duboin [1986].

The energy of both sources finally ends up in the neutral gas. During disturbedconditions the thermosphere is considerably heated at high latitudes. As interme-diate step the Joule heating also raises the ion temperature above 120 km, whereasthe soft precipitation leads to an increased electron temperature in the F-region.

98

The latter provides the main energy flow into the upper ionosphere. Since theenergy of electrons with E < 10 eV is thermalized, i.e. distributed to the ambientelectron gas, the heat flow can be estimated from the measured electron tempera-ture. For this purpose the equation of the thermal heat conduction of the electrons:

ce = - α Te5/2 ∂ Te

∂ h(16)

[α is the heat conduction coefficient] can be used which is divergent free:

∇ ce = 0 (17)

Since Eq. 16 contains only the electron temperature which is one of the basicparameters, the heat flow can be computed from the gradient of the Te-profile.Figure 5 shows heat flows for a one day experiment with the EISCAT-VHF-radar[Blelly and Alcaydé, 1994]. The enhanced flow events are caused by soft particleprecipitation whereas the almost constant "background" of about 20 µW.m-2 cor-respond to solar EUV-heating [the ionosphere is sunlit for 24 hours during May].

The actual electron density profile in the E- and D-region during precipitationevents depends strongly on the energy spectrum of the precipitating particles [forenergies E > 100 eV]. Therefore algorithms have been constructed to invert themeasured electron density profile into an energy spectrum [Vondrak and Baron,1977]. These algorithms have been considerably refined in recent years

Hea

t Flo

w [

µW

.m−

2 ]

00 06 12 18 00 060

10

20

30

40

50

60

70

Start : 910513 22:50 − End : 910515 06:45 [ UT ]

EISCAT − VHF F2 and Topside Heat Flows

F2

Topside

Figure 5. Heat flow into the topside ionosphere (1500 km) and into the F2-region (300 km) as a

function of time derived from EISCAT VHF measurements.

99

Figure 6. Electron density profile measured with EISCAT (left panel) and energy spectrum ofprecipitating electrons derived from it (right panel).The latter is compared to simulatneouslymeasuerd electron energy spectra from the VIKING satellite.

and can now take not only precipitating electrons but also protons into accountwhich mainly ionize in the D-region.

The inversion algorithm works in the following way: First a height profile ofthe electron production rate is computed from measured electron density profilesne(h) with the help of a simplified continuity equation:

p(h) = d ne (h)

d t + αeff ne2 (h) – pEUV (18)

For time series of the current variation one again uses height-integrated valuescomputed analogous to Eq. 9. Figure 3 [lower panel] shows an example for a 24-modeled [Kirkwood, 1993]. The production is on the other hand caused by pre-cipitating particles with energy fluxes f(E) and can therefore be written for elec-trons [e] and protons [p]:

p = sp fp (E) + se fe (E) (19)

where sp,e are the rate constants of various ionization reactions which are impor-tant in the height range under consideration.

The ionization rates of Eq. 19 are then fitted to the experimentally determined[Eq. 18] in a least-square sense by varying the fluxes at a number of fixed particleenergies E [e.g. assuming monoenergetic particles beams]. A typical result isshown in Figure 6 [Kirkwood and Osepian, 1995]. In the right panel the deducedenergy spectrum is displayed in comparison with flux data measured in-situ fromthe Viking satellite, in the right panel the electron density which was used to cal-culate the ionization rate [Eq. 18].

100

Figure 7. Neutral wind at 120 km altitude calculated for one day using different values for theion-neutral collision frequncy. The respective curves are a fits of the measured velocities to awind model assuming a diurnal and a semi-diurnal tide on top of a constant prevailing wind: U= A24cos(2π/24(t-P24))+A12cos(2π/12(t-P12))+A0.

5. Neutral atmospheric propertiesSince the IS-technique yields only plasma quantities, the estimate of parame-

ters of the neutral atmosphere involves some calculations and assumptions.

Relatively straight forward is the calculation of the neutral wind at E-regionheights. In a plane perpendicular to the magnetic field it follows from the ionmomentum [Eq. 2] for the zonal [Uz] and the meridional [Um] neutral wind com-ponents:

Uz = Vx -

Ωi

νin ( E + V x B )z

Um = Vy- Ωi

νin ( E + V x B )m

(20)

101

Here E is the electric field computed from Eq. 3 in the F-region, and V the vec-tor of the ion drift obtained from tristatic measurements at E-region heights. Thefactor Ωi/νin becomes considerably greater than unity above about 120 km. Thuserrors in the determination of E and V are strongly magnified for greater heights.In practice, the neutral wind can therefore be estimated with Eq. 20 only betweenabout 95 and 120 km, where the lower limit is usually determined by the poorsignal-to-noise ratio of the data.

As an example for neutral wind estimates Figure 7 shows the meridional [upperpanel] and zonal [lower panel] neutral wind component at 120 km altitude for afull day. It can clearly be seen that at night, when the SNR ratio is smaller thanduring daytime and consequently the accuracy of the measurements decreases, thescatter in the derived wind values considerably increases. The various curves inthe figure correspond to a fit of the wind pattern to a diurnal and a semidiurnaltide [see also section 6]. Since the value of νin is crucial for the computed magni-

tude of U, values departing by ± 30% from the model value [after MSIS 86] havealso been included in this figure [Kunitake and Schlegel, 1991].

At altitudes above the E-region a different technique has to be applied for aneutral wind estimate. A very simplified form of the momentum equation for theneutrals and ions parallel to the geomagnetic field can be written [Wickwar et al.,1984]:

V// = U// + Vd (21)

where:

Vd = - sin I νin

g + k

mi ne ∂ ∂ h

[ ne ( Te + Ti )]

is the ambipolar diffusion velocity along the direction of B [ I is the inclination of B, g is the acceleration of gravity and k is the Boltzman constant]. The meridi-onal component of the neutral wind can then be expressed as:

Um = Uv sec I - ( V// - Vd ) tan I (22)

Equation 21 contains apart from νin and mi only parameters that can be ob-tained with the IS-technique. The vertical neutral wind Uv is generally small andcan thus be neglected. Again νin is critical for these wind estimates [e.g. Burnsideet al., 1987]. In the F-region it consists of three different collision processes:

νin = νO+-O + νO+-N2 + νO+-O2 (23)

since O+ is the principal ion and N2, O2 and O are the most important neutralconstituents there.

102

Figure 8. Height profiles of measured ion drift parallel to B (Vi//), the ambipolar diffusion

velocity (Vd), the calculated meridional neutral wind (Um) and its vertical gradient.

Figure 9. Neutral wind in the thermosphere derived for a whole day from EISCAT CP-3 dataspanning a latitudinal range from 67° to 72°.

103

Figure 10. Neutral temperatures in the thermosphere derived simultaneously with the windvectors shown in Figure 9. The measured ion temperatures are also included.

Figure 8 shows an example of an Um-profile obtained in this way, together withthe measured V// and the computed Vd [Shibata and Schlegel, 1993].

An estimate of the zonal component of the neutral wind uz, is more compli-cated. A simplified form of the ion energy balance can to be used [St. Mauriceand Hanson, 1982]:

(Vy - Um)2 + (Vx - Uz)2 = 3 k mn

(Ti - Tn ) - mi + mn

mi νie

νin (Te - Ti ) (24)

with mn being the mass of the neutral particles, and νie the electron-ion collisionfrequency [e.g. Banks and Kockarts, 1973]. For the neutral gas temperature onecan either insert model values or Ti ≈ Tn can be used as a first approximation.

If a longer series of good quality data points are available, Eq. 24 can be usedto fit both the zonal wind and the neutral gas temperature [Alcaydé and Fon-tanari, 1986]. Figure 9 shows a clock-dial plot of neutral wind vectors for a whole24-hour period derived in this way from EISCAT-CP3 data spanning over a latitu-dinal range between 60° and 72.5°. Figure 10 contains the simultaneously ob-tained neutral temperatures together with the measured ion temperature.

104

Figure 11. MEM spectra of TIDs present in the electron density (Ne), in the line-of-sight ion

drift (Vi), in the ion temperature (Ti) and in the electron temperature (Te) for several heights.

The dashed lines indicate the bandwidth of the filters which have been used in the subsequentanalysys.

105

If either neutral wind or neutral temperature data are provided by a differenttechnique the missing quantity can also be calculated with the help of Eq. 22 and24 [e.g. Thuillier et al., 1990].

Neutral gas temperatures in the E-region can well be estimated from the as-sumption of Te ≈ Ti ≈ Tn which is valid during geomagnetic quiet conditions [e.g.Kirkwood, 1986]. Temperature differences between the three species are quicklyequalized due to frequent collisions.

6. TIDs and Gravity WavesTraveling ionospheric disturbances [TIDs] can most often be interpreted as the

ionospheric signatures of gravity waves in the neutral atmosphere [Hocke andSchlegel, 1996]. They appear as wave-like fluctuations in all basic ionosphericparameters. A first step in the investigation of these wave phenomena is the de-termination of their wave frequency. This can be performed either by using a Fou-rier transformation [FFT] or the maximum entropy method [MEM] [e.g. Ulrychand Bishop, 1975]. The latter is usually preferred because it yields reliable resultsfor shorter time series than the FFT which in principle assumes an infinite timesequence. Figure 11 shows such MEM-spectra of fluctuations in the basic pa-rameters for 21 height steps between 147 and 587 km.

In order to make the TIDs more clearly visible in the data, digital filtering [withButterworth filters] is applied [e.g. Hocke, 1994]. The width of the correspondingfilter has to be adjusted in a way that the peak of the fluctuation frequency fitsinto its range.

Figure 12 shows filtered data of the ion velocity and the electron density. Thecorresponding filter width is indicated in Figure 11 as two dashed lines around themain frequency peak. The forward tilting of the wave fronts indicate a gravitywaves as cause for the observed TID.

In a further treatment of the filtered data, amplitude profiles can be computedand profiles of phase relationship between the waves in the different parameterscan be established. Figure 13 shows an example [Hocke et al., 1995]. These phaserelationships provide insight into the interaction processes between the neutralgas and the plasma and in turn clues for the determination of the cause of the TID.A gravity wave as the cause can for instance be uniquely identified [Kirchengastet al., 1995].

106

Figure 12. Waves in the line-of-sight ion drift velocity (upper panel) and in the electron density(lower panel) made visible by digital filtering of the respective time series. The bandwidth of thefilter is indicated by dashed lines in Figure 11.

107

Figure 13. Upper panel:Average amplitude profiles of 45 TIDs in the four basic parameters.The boxes indicate the middle quartile of the data, the full dot the arithmetic mean. Lower pa-nel: Average phase relationships between the TIDs in the four basic parameters.

108

Figure 14. Comparison of measured (EISCAT) and modeled (GIFTS-Model) TIDs in the fourbasic parameters.

With some caution the wave frequency of the TID-fluctuations can be regardedas the wave frequency of the causing gravity wave. It has to be kept in mind,however, that a Doppler shift due to a neutral wind may be present which can beexpressed as:

ωD = k . U (25)

109

Figure 15. Amplitudes in the neutral temperature and in the neutral wind of the gravity wavewhich caused the TIDs displayed in Figure 14. These are results of the modeling process descri-bed in the text.

The fact that the frequency peak in Figure 13 is not at the same location at allheight steps is most probably due to such Doppler shifts and indicate wind shears.

The direct calculation of other parameters of the TID-causing gravity wave isgenerally not possible from IS-data. The interactions between the neutral gas andthe plasma are very complex so that no unique relationships exist between thegravity wave parameters [vertical and horizontal wave numbers, neutral gasfluctuations] and the plasma quantities. Instead, a modeling approach has turnedout to be promising [Kirchengast et al., 1995]. With a realistic ionospheric model[Kirchengast, 1992] the response of the plasma to a neutral atmospheric wave iscalculated and the results are compared to measured TIDs. By varying the gravitywave parameters a best agreement between the measured and the model data canthus be achieved. Figure 14 shows as an example measured and calculated TIDsin a representation similar as Figure 12. The wave parameters of the neutral gasobtained in this way are displayed in Figure 15. This method yields very reliableresults for gravity wave parameters but is rather time consuming. For a quick lookpurpose a reasonably realistic but very easy to handle algorithm has been devel-oped for such a modeling approach [Wuttke, 1994].

110

Figure 16. Example of a bi-spectrum to establish non-linear interaction of atmospheric waves.The contours indicate that (among others) the following frequency relationships exist:0.01 + 0.017 = 0.027 0.01 + 0.027 = 0.037 0.027 + 0.04 = 0.067 (all in min-1)

TIDs and gravity waves in a wavelength range between about 15 minutes[Brunt-Väisälä period] and a few hours can be studied with the method describedabove. It has also been successfully applied to atmospheric tides which constitutewaves with the period of one day and higher harmonics, e.g. 12 h, 8 h, 6 h etc.[Hocke, 1995; Virdi and Williams, 1993].

For studies of the propagation of TIDs and gravity waves other techniques haveto be used in addition to the IS measurements [e.g. Williams et al., 1993].

Waves in the thermosphere are frequently subject to non-linear interactions. Amethod for a quantitative examination of such an interaction which was originallyderived for sea-wave coupling has been successfully applied to atmosphericwaves [e.g. Rüster, 1992; Ma and Schlegel, 1991]. This technique uses the factthat the bi-spectrum defined by Eq. 26:

B ( ω1,ω2 ) = ⌡⌠

⌡⌠

R ( τ1,τ2 ) exp -i (ω1 τ1 + ω2 τ2) dτ1 dτ2 (26)

[where: R ( τ1,τ2 ) = X ( t ) X ( t + τ1 ) X ( t + τ2 ) is the third order moment of thetime series X(t) ],

is different from zero only if a phase relationship exists between three differentwaves with frequencies ω1, ω2, ω3 and the conditions:

111

ω1 ± ω2 ± ω3 = 0

k1 ± k2 ± k3 = 0(27)

hold. Whereas the determination of the wave vector k is not possible from IS-data,different values of ω can usually be determined in a measured time series, as out-lined above. Figure 16 shows an example of the bi-spectrum of three waves withvarious wave periods [Ma and Schlegel, 1993].

7. Ion temperature anisotropyHigh electric fields which drive the ions through the neutral gas creating large

differences in the velocity between both species, also cause a non Maxwellianvelocity distribution of the ions and in turn ion temperature anisotropies.

It was shown theoretically that in such a case the ion temperatures measuredparallel and perpendicular to the geomagnetic field B are different [St-Mauriceand Schunk, 1977]. Both temperatures can be expressed as:

T// = Tn ( 1 + β// D’2 )

T⊥ = Tn ( 1 + β⊥ D’2 ) (28)

where

D’ =| V - U | / 2 k Tn

mn

is the normalized differential velocity and Tn is the neutral temperature. β// and

β⊥ are to a first approximation constants depending on the collision model and themass ratio of ions and neutrals.

Ti// can be directly measured with the EISCAT-Tromsø radar looking parallel toB [CP-1 mode]. A direct measurement perpendicular to B is not possible, butfortunately experiments from Kiruna and Sodankylä provide two independenttemperature "components". The radar wave vector from both sites intersects withthe geomagnetic field at different angles ϕ . Using a general relationship derivedby Raman et al. [1981]:

Tiϕ = Ti⊥ sin2ϕ + Ti// cos2ϕ (29)

the temperatures measured from both sites can be expressed as functions of Ti//

and Ti⊥ . Therefore from a tri-static EISCAT experiment three independent esti-mates Tiϕ of the ion temperature can be obtained. With Eq. 28 and 29 the three

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Figure 17. Ion temperatures measured from Tromsoe, Kiruna and Sodankylae plotted as afunction of prevailing ion drift perpendicular to the geomagnetic field vector. The dashed curvesindicate expected temperatures if a Maxwellian ion velocity distribution is assumed, the dottedand the solid curves are for two different bi-Maxwellian velocity distributions.

unknowns Tn , β|| and β⊥ can then be calculated. By comparing the derived values

of the parameters β|| and β⊥ with those predicted by the kinetic theory, informa-tion about the ion-neutral interaction can be gained [e.g. Hubert, 1984]. Figure 17shows as an example ion temperatures measured from the three EISCAT sites incomparison with computed results from different assumptions about the ion ve-locity distribution [Glatthor and Hernandez, 1990]. It is obvious from this figurethat non-Maxwellian effects become important only for E x B drifts well above500 m/s.

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8. Coherent StructuresPlasma instabilities excited in the ionosphere create localized electron density

structures with different scales in space and time. Such structures are usually in-vestigated with VHF-radars providing a coherent integration. Since IS-facilitiesare in fact very powerful and sensitive coherent radars, it is easily possible to usethem for such studies. A problem in these investigations is that many of the un-stable plasma waves constituting the density structures propagate almost perpen-dicular to the geomagnetic field direction. The radar wave vector has thus to bedirected almost perpendicular to B which cannot be easily achieved from geomet-rical considerations. EISCAT for instance was deliberately placed in a valley withrelatively high mountains to the north in order to prevent contamination of theorders of magnitudes weaker incoherent scatter from strong coherent scatter. Thuswith the EISCAT system only angles of about 85° with respect to B can be real-ized. Although the backscatter from coherent structures decreases considerablywith the deviation angle from 90°, it can easily be received with an IS-facilitybecause of the large transmitter power and the high antenna gains [compared to ausual coherent radar].Another fact which has to kept in mind is that the radarfrequency of an IS facility is usually considerably higher than those of a coherentVHF radar. Thus the irregularities are probed at scale lengths:

l = λradar

2 (30)

which are usually smaller than 1 m.

The great advantage of IS facilities besides the higher sensitivity, is the muchbetter spatial resolution of the measurements compared to those of a usual coher-ent radar, because of the large antenna aperture. Figure 18 shows as an examplebackscatter contours as a function of range [height] and time in the E-regionwhich prove this ability [Schlegel et al., 1990]. It also enables accurate measure-ments of the aspect angle sensitivity [Moorcroft and Schlegel, 1990].

Similar as in the IS case, the spectral shape of the signal scattered from coher-ent structures can be measured as well as its Doppler shift. Unfortunately thereexists no theory so far to explain this spectrum quantitatively. Whereas the Dop-pler shift can be interpreted straight forward as the phase velocity of the unstableplasma waves, the width of the spectrum provides only some indirect informationabout the lifetime of the irregularities. Figure 19 shows an example of such meas-ured Doppler spectra [Mc Crea et al., 1991].

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Figure 18. Contours of backscattered power from coherent structures in the ionospheric E-region which are caused by the modified two stream plasma instability.

Figure 19. Three different Doppler spectra from coherent structures which are caused by unsta-ble plasma waves, excited by the modified two stream plasma instability. The numbers on theright of each spectrum indicate the backscattered power, the Dopller shift, the width and theskewness.

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Figure 20. Profiles of IS spectra (10 sec integration) measured along the geomagntic field sho-wing enhanced shoulders caused by coherent scatter.

Coherent echoes created by plasma instabilities are not only observed at E-region heights but also in the F-region [e.g. Lockwood et al., 1988]. Some of themare assumed to be caused by the ion-acoustic instability. The corresponding un-stable plasma waves propagate parallel B an can therefore be easily detected withan IS facility. In fact they can contaminate the usual IS spectrum by raising one ofits shoulder. Figure 20 shows such an example [Rietveld et al., 1991]. Suchasymmetric echoes have also been observed in the top-side ionosphere [Wahlundet al., 1993].

Another class of coherent echoes which have been very successfully studiedwith incoherent scatter facilities are the polar mesospheric summer echoes[PMSE]. They arise most probably from processes within the "dusty" plasmaaround 80-90 km [Röttger et al., 1990].

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9. ReferencesAlcaydé D. and J. Fontanari, Neutral temperature and winds from EISCAT CP-

3 observations, J. Atmos. Terr. Phys., 48, 931-947, 1986.

Araki T., K. Schlegel, and H. Lühr, Geomagnetic effects of the Hall and Peder-sen current flowing in the auroral ionosphere, J. Geophys. Res., 94, 17185-17199, 1989.

Banks P.M. and G. Kockarts, Aeronomy, Academic Press, New York and Lon-don, 1973.

Baron M.J. and R.H.Wand, F-region ion temperature enhancements resultingfrom Joule heating, J. Geophys. Res., 88, 4114-4118, 1983.

Blelly P.-L. and D. Alcaydé, Electron heat flow in the auroral ionosphere in-ferred from EISCAT-VHF observations, J. Geophys. Res., 99, 13181-13188,1994.

Bostrøm R., Electrodynamics of the ionosphere, in Cosmical Geophysics, Ed. A.Egeland, O. Holter, A. Omholt, Universitetsforlaget, Oslo, Bergen, Tromsø,1973.

Brekke A. and J. Moen, Observations of high latitude ionospheric conductances-a review, J. Atmos. Terr. Phys., 55, 1493-1512, 1993.

Burnside R.G., C.A. Tepley and V.B. Wickwar, The O+-O collision cross sec-tion: Can it be inferred from aeronomical measurements, Ann. Geophys., 5,343-349, 1987.

Cierpka K. and K. Schlegel, Parametric model simulations of gravity wave at-tenuation in the ionospheric F2-layer, submitted to J. Atmos. Terr. Phys., 1995.

Duboin M.L., Heating rates measured by EISCAT: latitudinal variations, J. At-mos. Terr. Phys.,48, 921-930, 1986.

Fontaine D., S. Perraut, D. Alcaydé, G. Caudal and B. Higel, Large scale struc-tures of the convection inferred from coordinated measurements by EISCATand GEOS 2, J. Atmos. Terr. Phys., 48, 973-986, 1986.

Glatthor N. and R. Hernández, Temperature anisotropy of drifting ions in theauroral F-region, observed by EISCAT, J. Atmos. Terr. Phys., 52, 545-560,1990.

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Hargreaves J.K., The solar-terrestrial environment, Cambridge Univ. Press,Cambridge, 1992.

Hocke K., Untersuchung des Phasen- und Amplitudenverhaltens von "travellingionospheric disturbances" mit Hilfe von EISCAT-Daten, Thesis, MPAE-W-05-94-12, Katlenburg-Lindau, 1994.

Hocke K., K. Schlegel and G. Kirchengast, Phases and amplitudes of TIDs inthe high-latitude F-region observed by EISCAT, J. Atmos. Terr. Phys., 57, inpress, 1995.

Hocke K., Tidal variations in the high latitude E- and F-region observed byEISCAT, Ann. Geophys., in press, 1995.

Hubert D., Non-Maxwellian velocity distribution functions and incoherent scat-tering of radar waves in the auroral ionosphere, J. Atmos. Terr. Phys., 46, 601-611, 1984.

Kelley M.C., The earth’s ionosphere, Academic Press, San Diego, 1989.

Kirchengast G., R. Leitinger, and K. Schlegel, A high-resolution model for theionospheric F-Region at mid- and high-latitude sites, Ann. Geophys., 10, 577-596, 1992.

Kirchengast G., K. Hocke and K. Schlegel, The gravity wave-TID relationship:Insight via theoretical model-EISCAT data comparison, J. Atmos. Terr. Phys.,57, in press, 1995.

Kirkwood S., Seasonal and tidal variations of neutral temperatures and densitiesin the high latitude lower thermosphere measured by EISCAT, J. Atmos. Terr.Phys., 48, 817-826, 1986.

Kirkwood S., Modeling the undisturbed high-latitude E-region, Adv. Space Res.,13(3), 102-104, 1993.

Kirkwood S. and A. Osepian, Quantitative studies of energetic particle precipi-tation using incoherent scatter radar. J. Geomagn. Geoelectr., 47, 783-799,1995.

Kunitake M. and K. Schlegel, Neutral winds in the lower thermosphere at highlatitudes from five years of EISCAT data, Ann. Geophys., 9, 143-155, 1991.

Lathuillere C. W. Kofman and B. Pibaret, Incoherent scatter measurements inthe F1-region, J. Atmos. Terr. Phys. ,48, 857-866, 1986.

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Lockwood M., K. Suvanto, J.-P. St.-Maurice, K. Kikuchi, B.J.I. Bromage,D.M. Willis, S.R. Crothers, H. Todd and S.W.H. Cowley, Scattered powerfrom non-thermal, F-region plasma observed by EISCAT – evidence for coher-ent echoes? J. Atmos. Terr. Phys., 50, 467-485, 1988.

Lühr H., H. Geisler and K. Schlegel, Current density models of the eastwardelectrojet derived from ground-based magnetic field and radar measurements, J.Atmos. Terr. Phys., 56, 81-91, 1993.

Ma S.Y. and K. Schlegel, Nonlinear wave-wave interaction related to gravitywave reflection in the auroral upper F-region with the EISCAT radar, J. Atmos.Terr. Phys., 55, 719-738, 1993.

McCrea I. W., K. Schlegel, T. Nygren, and T. B. Jones, COSCAT, a new auro-ral radar facility on 930 MHz - System description and first results, Ann. Geo-phys., 9, 461-469, 1991.

Moorcroft D. R. and K. Schlegel, Height and aspect sensitivity of large aspectangle coherent backscatter at 933 MHz, J. Geophys. Res., 95, 19011-19021,1990.

Murdin J., EISCAT UHF Geometry, KGI-Report, No 79:2, Kiruna, 1979.

Raman R.S.V., J.-P. St-Maurice, and R.S.B. Ong, Incoherent scattering of radiowaves in the auroral ionosphere, J. Geophys. Res., 86, 4751-4762, 1981.

Rietveld M.T., P.N. Collis and J.-P. St-Maurice, Naturally enhanced ion acous-tic waves in the auroral ionosphere observed with the EISCAT 933-MHz radar,J. Geophys. Res., 96, 19291-19305, 1991.

Röttger J., M. T. Rietveld, C. La Hoz, T. Hall, M. C. Kelley, and W. E.Swartz, Polar mesosphere summer echoes observed with the EISCAT 933-MHz radar and the CUPRI 46.9-MHz radar, their similarity to 224-MHz radarechoes, and their relation to turbulence and electron density profiles, RadioSci., 25, 671-687, 1990.

Rüster R., VHF radar observations in the summer polar mesosphere indicatingnon-linear interaction, Adv. Space Res., 12(10), 85-88, 1992.

Schlegel K., Reduced effective recombination coefficient in the disturbed polarE-region, J. Atmos. Terr. Phys., 44, 183-185, 1982.

Schlegel K., T. Turunen, and D. R. Moorcroft, Auroral radar measurements at16-cm wavelength with high range and time resolution, J. Geophys. Res., 95,19001-19009, 1990.

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Schunk R.W., Transport equations for aeronomy, Planet. Space Sci., 23, 437-485, 1975.

Schunk R.W. and A.F. Nagy, Electron temperatures in the F-region of the iono-sphere: Theory and observations, Rev. Geophys. Space Phys., 16, 355-399,1978.

Senior C., D. Fontaine, G. Caudal, D. Alcaydé, and J. Fontanari, Convectionelectric fields and electrostatic potential over 61 < l < 72 invariant latitude ob-served with the EISCAT facility. 2. Statistical Results, Ann. Geophys., 8, 257-272, 1990.

Shibata T. and K. Schlegel, Vertical structure of AGW associated ionosphericfluctuations in the E- and lower F-region observed with EISCAT – a casestudy, J. Atmos. Terr. Phys., 55, 739-749, 1993.

St-Maurice J.-P. and R.W. Schunk, Auroral ion velocity distributions for apolarization collision model, Planet. Space Sci., 25, 243-260, 1977.

St-Maurice J.-P. and W.B. Hanson, Ion frictional heating at high latitudes andits possible use for an in-situ determination of neutral thermospheric winds andtemperatures, J. Geophys. Res., 87, 7580-7602, 1982.

Thuillier G., C. Lathuiliere, M. Herse, C. Senior, W. Kofman, M. L. Duboin,D. Alcaydé, F. Barlier, and J. Fontanari, Coordinated EISCAT-MICADOinterferometer measurements of neutral wind and temperature in E- and F-regions, J. Atmos. Terr. Phys., 52, 625-636, 1990.

Ullrych T. J. and T. N. Bishop, Maximum entropy spectral analysis and autore-gressive decomposition, Rev. Geophys. Space Phys., 11, 183-200, 1975.

Virdi T.S. and P.J.S.Williams, Altitude variations in the amplitude and phase oftidal oscillations at high latitude, J. Atmos. Terr. Phys., 55, 697-717, 1993.

Vondrak R.R. and M. Baron, A method of obtaining the energy distribution ofauroral electrons from incoherent scatter radar measurements, In: Radar Prob-ing of the Auroral Plasma, Ed. A. Brekke, Universitetsforlaget, Oslo, 1977.

Wahlund J.-E., H.J. Opgenoorth, F.R.E. Forme, M.A.L. Persson, I. Hägg-ström and J. Lilensten, Electron energization in the topside auroral iono-sphere: on the importance of ion-acoustic turbulence, J. Atmos. Terr. Phys., 55,623-696, 1993.

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Wickwar V.B., J.M. Baron and R.D. Sears, Auroral energy input from energeticelectrons and Joule heating at Chatanika, J. Geophys. Res., 80, 4364-4367,1975.

Williams P.J.S., T.S. Virdi, R.V. Lewis, M. Lester, A.S. Rodger, I.W. McCreaand K.S.C. Freeman, Worldwide Atmospheric gravity-wave study in theEuropean sector 1985-1990, J. Atmos. Terr. Phys., 55, 683-696, 1993.

Wu J. and C. Taieb, Observations of the structure of the thermospheric relativecomposition n(H)/n(O) with the EISCAT-VHF radar, Ann. Geophys., 11, 485-493, 1993.

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SOLAR WIND - MAGNETOSPHERE COUPLING

Mike Lockwood

1. IntroductionThe solar wind brings energy, mass and momentum from the sun to the Earth.

The geomagnetic field deflects the flow of plasma to generate the low densitycavity that is the magnetosphere. The efficiency of the mechanisms by which themagnetosphere extracts some of the mass, energy and momentum of the passingsolar wind are critically dependent on the orientation of the interplanetary mag-netic field [IMF]. This is a weak field of solar origin which is embedded in thesolar wind plasma. This review begins with a brief survey of the properties of theinterplanetary medium, in which the Earth’s magnetosphere is immersed [section2]. The uses of the approximate, but self-consistent, formalism of magnetohydro-dynamics [MHD] are then discussed in section 3, in particular the application ofthe "frozen-in flux" concept to the large-scale, high-conductivity magnetoplasmasin interplanetary space, the magnetosphere and the upper ionosphere. Were it toapply everywhere, frozen-in would allow very little transfer from the solar windto the magnetosphere and much of the fascination of the coupled magnetosphere-ionosphere-thermosphere system would be lost. Fortunately, that is not the case,largely because of the phenomenon of magnetic reconnection, a localised break-down of the frozen-in theorem. Reconnection is not just a curiosity of solar-terrestrial physics, it is a process which has considerable implications in otherdisciplines in science, for example astrophysicists believe it removes magneticflux from proto-stars which would otherwise prevent them from condensing. OnEarth, reconnection is both a nuisance and a help for researchers developingplasma fusion reactors, causing loss of confining field in tokomaks but allowingthe development of large fields in devices called spheromaks. Solar-terrestrialphysics [STP] is the discipline which developed the concept of reconnection andremains vital in its continued study, partly because it can be probed using acombination of remote sensing techniques [such as radars, magnetometers andoptical imagers] and in-situ observations [such as spacecraft particle detectors].Section 4 reviews the nature of the boundary separating the magnetosphere andinterplanetary space, called the magnetopause. This is the interaction regionwhere the extraction of mass energy and momentum takes place. Particularemphasis is placed on the experimental evidence for magnetopause reconnection,which is the dominant process which facilitates this extraction. In section 5 wewill look at the subsequent transfer from the magnetopause to the ionosphere,including the key role of field-aligned currents in the energy and momentumtransfer. The resulting effects in the ionosphere in the cusp region, the magneticprojection of the magnetopause are discussed in section 6, including the velocity

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filter effect of the precipitating particles. In all these discussions, there will be atendency to describe the steady-state cases because they are simplest. We do not,as yet, know of any long-term trends in the coupled magnetosphere-ionosphere-thermosphere system, and so if we average over sufficiently long periods [thetime scale involved depending on the phenomenon in question], then we effec-tively produce a steady-state description. However, in recent years, there has beenmuch interest in phenomena which take place on time scales that are too short forthe system to be considered an equilibrium one, i.e. when steady state does notapply. Two key examples are the substorm cycle and the effects of transientbursts of magnetopause reconnection. Section 7 discusses how the steady-stateconcepts can be generalised to allow for this.

2. The characteristics of interplanetary space at theEarth’s orbit

The hot solar corona ejects the supersonic solar wind. This process iscontinuous but still highly structured in time a space. Regions which appear darkin X-ray images of the sun are called coronal holes, and these regions of relativelythin coronal atmosphere are sources of enhanced solar wind in both speed anddensity. In addition, there are large coronal mass ejection events, these are seenevery 2 days on average, and typically contain 1013 kg of plasma, move at about500 km s-1 and carry 5 × 1018 W of power. On average, the solar wind powerdensity is about 3 × 10-4 W m-2, impinging on the Earth’s magnetosphere whichpresents a cross sectional area of about π(15 RE)2 ≈ 3 × 1016 m2 , giving a totalincident power of about 10 13 W, of which only a few percent is extracted by themagnetosphere. [Note, distances in the magnetosphere are usually quoted inunits of an Earth radius, 1RE = 6370 km]. To put these powers into some kind ofperspective, mankind currently uses of order 1013 W from all sources while thereis of order 2 x 1017 W incident on the Earth in the form of solar electromagneticradiations, of which roughly 1/3 is reflected back into space.

largest smallest mode

solar wind density, Nsw (m-3) 8.3 × 107 ~ 0 6 × 106

solar wind velocity, Vsw (km s-1) 950 250 370

IMF field strength, BIMF (nT) 85 ~ 0 6

IMF Bz (GSM) (nT) 27 -31 0

Table 1. Characteristics of the interplanetary medium at the orbit of the Earth (at an Astro-nomical Unit , 1AU, from sun)

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In a survey of over 105 hourly averages of measurements of interplanetaryspace at the Earth’s orbit, taken over two solar cycles, Hapgood et al. [1991] givethe distributions of key solar wind and IMF parameters. Table 1 summarises thesedistributions by giving the largest and smallest recorded values and the mostcommon value [i.e. the mode of the distribution].

In all cases the interplanetary medium shows great variability. The Bzcomponent of the IMF is the northward component in the GSM [Geocentric SolarMagnetospheric] coordinate system. It will later be explained how thiscomponent is a key factor controlling the transfer of solar wind energy, mass andmomentum across the magnetopause. In the GSM coordinate system, the Xcomponent points from the Earth to the sun; Z is northward along the projectionof the Earth’s dipole axis onto the YZ plane [normal to X] and Y makes up theright hand set and points roughly towards dusk. The distribution of Bz [GSM] issymmetric about zero and so half the time the IMF points northward and half thetime it is southward.

3. MagnetohydrodynamicsIn a plasma, free electrically-charged particles can move relative to each other,

such that a current flows. This current alters the magnetic field at all points in thecosmos, but the effect is strongest close to where the current flows. However, theinteraction is a coupled one, because the magnetic field influences the motion ofthe charged particles, via the Lorentz force. Magnetohydrodynamics [MHD] is aset of equations, given here in their simplest form, which provides a self-consistent description of the behaviour of this coupled magnetoplasma. As itsname implies, it is a fluid description and does not deal with individual particles,as would a kinetic approach. The advantages and limitations of MHD will bediscussed in 3-5.

Before discussing MHD, it is worth remembering some central tenants ofelectromagnetism. Equations for the electric and magnetic fields [ E and B ,respectively] can be derived from the relativistic Lorentz frame transformationsfor force and distance applied to the electrostatic force between two chargedparticles [e.g. Lorrain and Corson, 1970; Jackson, 1975]. In the non-relativisticlimit, E and B can then be shown to transform from reference frame 1 to frame 2,where frame 2 moves at velocity U in frame 1, according to:

B2 = B1 (1)

E2 = E1 + U × B (2)

This shows that the magnetic field is the same in any reference frame. It hasbeen argued that this means that it also makes no sense to consider moving field

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lines. To some extent, this may be true, but then it makes even less sense to arguethat they must therefore be still, as that is simply the zero speed limit of themoving case! A better interpretation is that Eq. 1 allows us, at the non-relativisticspeeds involved in most STP phenomena, to consider field lines as moving at anyspeed, including zero, as we wish. If we correctly describe the motions of chargedparticles, then that is all that field theory is intended to do. Note that if B isindependent of frame so, by Ampère's law, must the current density J be also.This is reasonable, as current is the difference in fluxes of oppositely chargedparticles and this difference will be frame independent. The electric field, on theother hand varies with reference frame. Therefore we should always make it clearwhich frame any electric field estimate is measured in. Notice also that Eq. 2shows that it is always possible to define a frame velocity U such that E is zero.

3.1. Ohm’s Law for a plasmaIf we take the momentum balance equation for the gas of any one species k

[density Nk, Pressure Pk, bulk flow velocity vk, mass mk and charge qk] in aplasma:

Nkmk ∂ vk

∂ t = ∇ Pk + Nk mk g + Nk qk [E + v k× B] - Σj≠k F kj (3)

the left hand side [LHS] is the inertial term, and the terms on the right hand side[RHS] are, in order, due to the pressure gradient, gravity, the Lorentz force andthe frictional force due to collisions with all other species, j [g is the accelerationdue to gravity, and e the electronic charge]. The force on the electrons due to theions, Fei is given by:

Fei = ϑei me (v e - v i ) = - Fie (4)

where ϑei is the electron-ion collision frequency. The current density, J, is givenby:

J = Ne e (vi - ve ) = - Ne e Fei

ϑei me . (5)

We define the plasma velocity as the weighted [by mass] mean of the electronand ion bulk flow velocities:

V = m ev e + mi v i

me + mi (6)

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We here take the simplest case of a plasma with only one ion species, negligiblecollisions with neutrals and no pressure gradients [all of which can be general-ised at the expense of complexity; see Alfvén and Fälthammar, 1963]. Taking Eq.3 for an electron gas [×-me] and for an ion gas [× mi], adding the two expressionstogether and then substituting from Eq. 4, 5 and 6 we get the commonly usedform of Ohm’s law:

J = Ne e2

( ϑeime) [E + V × B] = σ [E + V × B] (7)

where σ is called the electrical conductivity. From Eq. 2 the term in squarebrackets in Eq. 7 is the electric field in the rest frame of the plasma [in which V iszero]. It should be remembered that this form is only approximate and has ne-glected pressure gradients and collisions with neutrals. As a result of the latterassumption, it is invalid in the lower ionosphere where there are considerableHall and Pedersen conductivities introduced by collisions with neutrals. We hereuse it in the upper "F-region" ionosphere, the magnetosphere and in interplane-tary space.

3.2. The induction equation and frozen-in fluxIf, in addition to Ohm’s law [Eq. 7], we use three of Maxwell’s equations,

namely the non- existence of magnetic monopoles, Ampère's law [for a goodconductor such that the displacement current can be neglected] and Faraday'slaw in differential form:

∇ B = 0 (8)

× B = µo J (9)

∂ B∂ t = - ( × E) (10)

where µo is the permeability of free space. If we substitute using Eq. 9 and 10

into Eq. 7 and use Eq. 8 and the vector expression ×(×B)=(.B)-∇ 2B, wecan derive the induction equation:

∂ B∂ t = × (V × B ) +

∇ 2 B µo σ

. (11)

The first term on the RHS is called the convective term and the second is thediffusive term. The ratio of the convective term divided by the diffusive term iscalled the magnetic Reynolds number Rm which, from dimensional analysis, isgiven by the order of magnitude expression

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Rm = × (V × B ) µo σ∇ 2 B ~ µo σ Vc Lc (12)

where Vc is the characteristic scale speed of the plasma and Lc is its characteristicscale length.

How a magnetoplasma behaves depends critically on the magnitude of Rm. IfRm is very small [ « 1], the convective term can be neglected and the inductionequation [Eq. 11] reduces to a diffusion equation in which the field diffuses fromhigh to low values. On the other hand, in the limit where Rm » 1, the diffusiveterm can be neglected. To understand the behaviour in this limit, consider anyclosed loop in the plasma C, which bounds an area S. Using Eq. 11 in the Rm » 1limit, and then Stoke's theorem, the rate of change of flux threading that loop is

∂ F∂ t =

⌡⌠

S

∂ B∂ t .ds =

⌡⌠

S

× (V × B ).ds = O

⌡⌠

C

(V × B).dl (13)

If we think of field lines moving with the plasma velocity, V, the RHS ofEq. 13 would be the rate at which flux was convected across the line C whichwould thus equal to the rate of change of flux threading the loop. Given that thisis the RHS , this means that Eq. 13 shows us that in this very high Rm limit, themagnetic field does move with the plasma velocity V. This is Alfvén's famous"frozen-in flux" theorem, so called because the field and the plasma are frozentogether and move together.

Region σ (mhos m-1) Vc (m s-1) Lc (m) Rm

Base of corona 103 105 106 108

Solar Wind at 1 AU 104 105 109 1012

Magnetosphere 108 105 108 1015

Ionospheric F-region 102 103 105 104

Table 2. Typical order of magnitude estimates of the conductivity, σ, characteristic plasmavelocity Vc, scale length Lc , and magnetic Reynolds number, Rm

Table 2 shows typical order-of-magnitude values for various regions in thesolar-terrestrial system of all the terms in the approximate expression for Rm

[Eq. 12]. It can be seen that in all cases the Reynolds number is extremely large

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and thus we should expect frozen-in to be a valid approximation in all theseregions.

In order to understand the basic behaviour of the magnetoplasmas in thesevarious regions it is instructive to look at the relative densities of energy stored inthe magnetic field, the thermal motions of particles and the bulk flow of theplasma, these are given by, respectively, WB = B2/2µo [see section 5.1],Wth = N k T, and WV = m V2/2, where k is Boltzmann’s constant and T is theplasma temperature. Typical values are given in Table 3, for the same regions asin Table 2, except that the magnetosphere has been broadly sub-divided into thehigh density co-rotating inner torus called the plasmasphere and the low-densityconvecting outer region called the plasma trough.

Region Ions BnT

Vms-1

Nm-3

TK

Wth Jm-3

WVJm-3

WBJm-3

Base of Corona H+ 105 104 1015 106 10-2 10-4 10-2

1 AU H+ 5 5.105 5.106 5.104 10-12 10-9 10-11

M.spheretrough

H+ 50 105 104 107 10-12 10-13 10-9

Plasmasphere H+ 5.103 104 109 104 10-10 10-10 10-5

F-region O+ 5.104 103 1011 103 10-9 10-9 10-3

Table 3. Typical order of magnitude estimates of energy densities in various regions of thesolar-terrestrial system.

Where one energy density is clearly dominant, it has been underlined. In theinterplanetary medium, the dominant energy density is in the bulk flow of theplasma and, as a result, frozen-in means that the IMF is dragged along with thesolar wind flow. On the other hand, in the magnetosphere and F-region iono-sphere the dominant energy density is that of the magnetic field and thus frozen-in results in the field constraining the plasma.

The dominance of the field energy density is greatest in the ionosphere. Indeed,the ionospheric and magnetospheric particles have very little effect on the field atlow altitudes, that field being almost completely due to currents in the Earth’sinterior. As a result, the largest currents which flow as a part of STP phenomenacause magnetic perturbations of order 1000 nT, which is only 2% of theionospheric field caused by the interior currents [which is roughly constant atabout Bi = 5 × 10-5 T]. In the sense that the magnetic field is roughly constant, wesay that the ionosphere is incompressible. This is a very useful fact because themagnetic flux threading a certain region of the magnetosphere can change

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with time. Because the field is constant at low altitudes, the ionospheric signatureof such a flux variation will be a change in the area of the corresponding region inthe ionosphere.

3.3. E x B drift and motional electric fieldsFrom the induction equation [Eq. 11] in the Rm » 1 limit and Faraday's law

[Eq. 10]:

∂ B∂ t = × (V × B ) = - × E

E = - (V × B ) (14)

V = E × B

B2 (15)

Thus for a magnetoplasma for which frozen-in applies, an electric fieldcorresponds to a plasma motion perpendicular to both the applied electric andmagnetic fields at speed E / B, often referred to as the "E-cross-B drift". E isperpendicular to B, ie. there is no field-parallel electric field, E||, if frozen-inapplies strictly.

Note that Eq. 14 and 15 can be derived from Ohm's law for a plasma [Eq. 7] ifwe take the conductivity σ to be infinite, as then Eq. 14 must be true to avoid aninfinite current density. Hence the frozen-in approximation is sometimes referredto as the "infinite conductivity limit". However, as we saw in the last section, theapplicability of frozen-in to solar-terrestrial plasmas is really caused by the largescale lengths [Lc] as much as by their high conductivities. From Table 2, wewould expect the frozen-in approximation [and thus Eq. 14] to be least applicablein the F-region ionosphere. A recent paper by Hanson et al. [1994] demonstrateshow good an approximation this is, even in the F-region. They took satelliteobservations of E in the topside ionosphere from measurements of the potentialdifference between two probes on long booms and of known separation. Theycompared these with estimates of - (V × B) from magnetometer and ion driftmeter observations. The results showed an extraordinary level of agreement andany [small] differences that were found were shown to be caused by experimentaluncertainties.

Table 2 shows that frozen-in applies also in the interplanetary medium, wherethe solar wind flows with a plasma velocity Vsw in the Earth's frame of reference.From Eq. 14 there is no electric field in the rest frame of the solar wind flow [inwhich V is zero], but by Eq. 2 there will be an electric field of - (Vsw × BIMF ) in

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the Earth’s frame. Because it corresponds to a bulk flow of a frozen-in plasma,this is often referred to as the motional electric field of the interplanetary medium.The direction of the solar wind flow is always close to antiparallel to the X axis,so for southward IMF [Bz < 0], this electric field points from dawn to dusk [in the+Y direction].

It is here worth noting a point about the term "flux transfer", often used inmagnetospheric physics [e.g. Holzer and Slavin, 1979; Russell and Elphic, 1978].Faraday’s law [Eq. 10] in integral form is

O⌡⌠

C

E . dl =

∂F∂t

= ∂ ∂ t

⌡⌠

S

B . ds ( 16)

where F is the flux threading the area S bound by the circuit C. [Note: in theionosphere, incompressibility means that the RHS reduces to B (∂€A/∂€t) becauseB is constant and the area A must change if the flux F changes]. If we considertwo loops C and C1, which share a common segment across which there is a

voltage Φ but the tangential electric field along either loop is everywhere elseequal to zero, then from Eq. 10:

Φ = O⌡⌠

C

E . dl = - O

⌡⌠

C1

E . dl =

∂ FC

∂ t = - ∂ FC1

∂ t

where both line integrations are done in the same rotational sense. Thus the fluxthreading C1 decreases at the same rate Φ as the flux threading the adjoining loopC increases. The voltage along the common segment is therefore identicallysynonymous with a flux transfer rate from C to C1 [dimensionally, the unit volts isthe same as Wb s-1]. This is purely a consequence of Faraday’s law. If we are alsodealing with a frozen-in plasma, the plasma will also be transferred at the samevelocity as the magnetic field lines from within C1 to in C. We will later deal withevents called "flux transfer events" or FTEs, a name which sometime causesdisquiet: however from the above, it is identical in meaning to "voltage bursts".

3.4. The J x B and curvature forces and magnetic pressureIf we take the momentum equation [Eq. 3] for ions and add it to that for

electrons, using the definition of plasma velocity V [Eq. 6], the plasma densityρ = Ne (me + mi), the plasma pressure P = Pe + Pi , the current density J given by

130

Eq. 5 and charge neutrality [Ne = Ni], we get the force balance equation for theplasma:

ρ ∂ V∂ t - P - ρ g = [Ne e Ve - Ni e Vi] × B = J × B (17)

The term on the right is called the J × B force. If we substitute using Ampère'slaw Eq. 9 and use the vector relation [( × B) × B= ∇ 2 B / 2 + (B . ) B] we findthat the J × B force can be combined with the plasma pressure term thus:

P + J × B = - (P + B2

2µo) + (B . )

Bµo

(18)

from this we see that a magnetic pressure [B2/2µo] is added to the plasma pres-sure P [first term of RHS of Eq. 18], and there is a second force which acts nor-mal to B if the field lines have any curvature [from the second term of the RHS ofEq. 18]. This force vector lies in the plane of the curvature and acts so as to try tostraighten the curved field lines. For this reason, it is often referred to as the "ten-sion force". I prefer the term "curvature force" because a tension, as in stretchedelastic band, will remain when the band becomes straight, whereas the forcedescribed by Eq. 18 will vanish when the field lines are straight. The second termon the RHS also provides a term which exactly cancels the field parallel compo-nent of the first term. Thus the magnetic pressure acts only perpendicular to B.

3.5. Uses, advantages and limitationsMagnetohydrodynamics has the huge advantage of being a self-consistent

formalism. Application of a few simple rules is extraordinarily powerful, forexample, as in predicting the motion of field lines and frozen-in plasma as kinkedfield lines straighten under the curvature force. It does lead to a lot of what issometimes disparagingly referred to as "cartoon physics" because it empowers usto draw diagrams of field lines and from them deduce how they will behave. Aswith field theory, this has wide-ranging predictive power, as long as one obeysthe rules. Other formulations are far more likely to be in error because they do nothave the in-built consistency of MHD [see, for example, Owen and Cowley,1991]. One also hears the complaint that what is really out there in space aremoving, charged particles. This is a true statement, but rejection of MHD on thesegrounds is also a rejection of field theory and electromagnetism!

The major disadvantage of MHD is that it is a fluid approach and, as such, tellsus nothing about the behaviour of the individual electron and ion species.Therefore we have to graft on kinetic or semi-kinetic treatments to predictparticle distribution functions. An example of this type of hybrid theory isdiscussed here in section 4.5. A second, entirely separate, question involves the

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validity of the frozen-in approximation or "ideal MHD". This is an approximateformalism and does break down. Indeed, nearly all the fascination and beauty ofthe magnetosphere-ionosphere-thermosphere system stems from the fact that itdoes break down. With fully frozen-in plasmas there would be little energy, massand momentum transfer from the solar wind, no aurora, no ring current etc.However, in the same way that the existence of relativistic effects does not stopNewtonian mechanics from describing a myriad of phenomena and systems, sothe frozen-in approximation is valid for many regions and events of the solar-terrestrial system. The approach adopted here is one of using ideal MHD, withproper regard to where and how it can break down. It is an approach which hasgained almost universal acceptance for no other reason than its success indescribing the main features of the transfer from the solar wind to the ionosphere.Most importantly, it has enabled a large number of predictions to be made inadvance of observations - much more significant in science than the use of atheory to explain observations after they have been made. Examples of this arelegion, and include the basic prediction that the momentum and energy transferfrom the solar wind into the ionosphere is enhanced during southward IMF[section 5.5]. We will here also discuss some more detailed predictions whichhave been later proved correct, predictions concerning the distribution functionsof ion populations near the magnetopause [section 4.5] and cusp ion steps[section 7.3].

4. The magnetopauseFigure 1 is a noon-midnight cross-section of the magnetosphere at a time when

the IMF points southward [after Cowley, 1991]. We view from the dusk side sothat the sun is to the left and the GSM axes X, Y and Z are as shown. The solarwind [SW] flow is supersonic and super-Alfvénic and so the bow shock [BS]forms upstream of the obstacle presented by the Earth's magnetic field. Theboundary of the magnetosphere, the magnetopause MP is compressed on thedayside by the dynamic pressure of the solar wind flow and, for reasons discussedlater, the Earth's field is extended into a long tail on the nightside, very much asoriginally envisaged in Chapman and Ferraro's seminal [1931] paper. Theshocked interplanetary medium between BS and MP is called the magnetosheathMS. Currents flow in the magnetopause, called the Chapman-Ferraro currents,corresponding to the magnetic shear between the magnetosheath and themagnetosphere fields, Bsh and Bsp. The Chapman-Ferraro currents flow in the +Ydirection in the subsolar region, but in the -Y direction on the high-latitude tailmagnetopause [the high-latitude boundary layer or HLBL]. In three-dimensions,these currents circulate around the topology in the geomagnetic field we call themagnetic cusp.

132

E

E

L

L

S

J

S

E

E

J

Z

X Y

BS

MS

SWRC PSRC

XtX

IMF MP

Figure 1. A noon-midnight cross-section of the magnetosphere, viewed from dusk with thesun to the left. When the IMF is southward (Bz < 0), field lines (solid lines) are opened at themagnetopause reconnection site, X, and convect antisunward under the action of the solarwind electric field, E, which exists in the Earth’s frame of reference and everywhere pointsout of the plane of the diagram in the +Y direction. The flow of electromagnetic energy , orPoynting flux, S = E x B, is shown by the dashed lines. Unless otherwise marked, vectors intoand out of the plane of the diagram are currents. The open field lines are closed again byreconnection at the tail X-line, Xt. Labelled regions and boundaries are: solar wind SW;interplanetary magnetic field IMF; bow shock BS; magnetopause MP; magnetosheath MS;tail lobe L; the plasma sheet PS and its inner edge, the ring current RC. The dayside magne-topause (Chapman-Ferraro) currents are in the +Y direction, making J . E > 0, i.e. there is asink of S. At latitudes above the magnetic cusp, the currents are into the diagram, makingJ . E < 0, i.e. a source of S. In steady-state the energy extracted from the solar wind at thelobe magnetopause is deposited in the plasma sheet, ring current and the ionosphere. Duringsubstorm growth phases, the extracted energy is also stored in the tail as the lobe field andenergy density increase because open magnetic flux accumulates there. [After Cowley, 1991]

4.1. The magnetosheathBecause the field in the magnetosheath is usually weak, it is often ignored and

the fluid flow of the plasma described in "gas-dynamic" models of the sheath[Spreiter et al., 1966]. These show that the flow stagnates at the nose of themagnetosphere [where MP cuts the X axis] and here the plasma density N isroughly 4 times the value in the undisturbed solar wind, Nsw and the temperatureT is about 20 Tsw. Because there is no field, the sheath is symmetric about the Xaxis in these models and the flow speed just outside the magnetopause increaseswith distance from the nose. Where the boundary intersects the ZY plane [X=0],V≈0.7Vsw with N ≈ 1.5Nsw and T ≈ 12Tsw : at X= -10RE , V ≈ 0.85Vsw with N ≈0.8Nsw and T ≈ 7Tsw. Because V is lower near the nose of the magnetosphere, thefrozen in field lines in the real magnetosheath become draped over the nose of themagnetosphere, as in figure 1 [Crooker et al., 1985]. The sheath field at the

133

magnetopause, Bsh, thus becomes larger than in the IMF and is usuallycomparable to the interior field of the magnetosphere at the dayside boundary,Bsp. Both are typically 20 nT, but whereas Bsp will always point northward, Bsh

can have any direction parallel to the boundary, depending on the IMForientation. In an equilibrium situation, the enhanced dayside Bsh would cause anenhanced magnetic pressure, as shown by Eq. 18, and a corresponding decreasein the [anisotropic] particle pressure and density would be expected. This iscalled a plasma depletion layer [PDL] and is indeed observed, but only duringnorthward IMF [Phan et al., 1994]. This is the first indication that the system isnot in equilibrium, at least during southward IMF. The PDL is missing becauseBsh, and the dayside magnetosphere, are eroded by a process called magneticreconnection [discussed here in section 4.3] at a faster rate than that at which Bsh

can be increased by the draping effect of the solar wind flow.

4.2. Boundary motionsThe location of the dayside magnetopause is known to be closer to Earth if the

solar wind dynamic pressure is high and/or if the IMF has a southwardcomponent [Bz<0] [Maezawa, 1974; Roelof and Sibeck, 1993; Petrinec andRussell, 1993]. The solar wind pressure acts to compress the daysidemagnetosphere [and increase the Chapman-Ferraro currents], whilstincreasingly southward IMF increases the rate of magnetic reconnection [see nextsection] and this erodes the dayside magnetopause [Aubry et al., 1970], similar tothe erosion of the PDL. The variability of the solar wind dynamic pressure and ofthe reconnection process, on a wide range of time scales, means that themagnetopause is virtually always in motion. This was first clearly demonstratedby the two-satellite ISEE mission, and boundary speeds of typically 50 km s-1

were found by timing the observed magnetopause crossings at the two satellites[Russell and Elphic, 1978]. The magnetopause motions are often oscillatory suchthat the boundary may cross the satellite many times during any one pass.Typically, satellites move at about 2 km s-1 normal to the boundary and so anyone crossing is likely to be due to the boundary motion and not the satellitemotion [Hapgood and Lockwood, 1995].

This dynamic nature of the boundary makes observations of many of its char-acteristics difficult. In addition, the boundary distorts, making accurate determi-nation of the orientation of the boundary very difficult.

134

X

Bsp

B Bn n

E

v

v

B

J J

out

in

sh

2a

(a). (b).

(c). (d).

Figure 2. Magnetic reconnection between a southward-pointing magnetosheath field, Bsh,

and the northward- pointing magnetospheric field, Bsp, at the low-latitude magnetopause. In(a) frozen-in applies everywhere and there is no magnetic flux threading the sheet of magne-topause current, J (i.e. there is tangential discontinuity in the field). In (b) diffusion in alocalised disruption of the current sheet allows field lines to reconfigure such that they threadthe magnetopause, giving a boundary-normal field component Bn and a rotational disconti-nuity (RD). Outside of the diffusion region, frozen-in applies and field lines E x B drift intoand away from the reconnection site at Vin and Vout, under the influence of a boundary-tangential electric field, E, called the "reconnection rate". In Petschek reconnection E isconsiderably increased by shocks (shown as dashed lines in c) which stand in the inflow. Theangle of the outflow wedges, a, increases with E. A pulse of Petschek reconnection yields apair of bulges in the outflow layer which propagate away from the reconnection site (asshown in d), yielding bipolar signatures in the boundary-normal field which have oppositepolarity on opposite sides of the X-line.

4.3. Magnetic reconnectionFigure 2 considers the magnetopause at low latitudes on the dayside, near thesubsolar point in figure 1. If frozen-in applied strictly, Bsh and Bsp would be keptapart by the Chapman-Ferraro currents, as shown in 2a. However, this current

135

sheet would be squeezed between the thermal and magnetic pressure of the sheath[caused by the dynamic pressure of the solar wind] and the magnetic pressure ofthe magnetosphere. This would cause the current layer to thin, until the charac-teristic scale length, Lc would become small enough for the magnetic Reynoldsnumber to fall to near unity [Eq. 12]. From the induction Eq. 11, this means thatthe frozen-in approximation starts to break down and the field diffusion termbecomes important. The fields diffuse from high values to the low values at thecentre of the current sheet. The process of magnetic reconnection allows them toreconfigure at a singularity at the centre of the current sheet, as shown in figure2b, such that they thread the current sheet. These "open" field lines connect theinterplanetary space and the magnetosphere: they are highly kinked and areaccelerated away from the reconnection site by the curvature force. Away fromthe diffusion region, frozen-in applies and the motion of the Bsh and Bsp fieldlines towards the reconnection site [at speed Vin] and of the open field lines awayfrom it [at speed Vout] both correspond to an electric field out of the plane of thediagram, called the reconnection rate, E. This process is often also referred to as"merging": this is possibly a more accurate name in that it is very unlikely thatthe field lines are cut and then joined back together [reconnection implies a priordisconnection] as this would involve the existence of a magnetic monopole,however briefly. However, I here use the term "magnetic reconnection" becausethat is what it is called in all other branches of plasma physics and also becausethat is the name given by Dungey [1953; 1961] who was the first to describe thisprocess in this way and to understand its implications for the terrestrial plasmaenvironment. It can be shown that the reconnection rate is much faster if a pair ofshocks form and stand in the inflow region, as shown by the dashed lines in 2c,this is called Petschek reconnection [see review by Petschek, 1995]. The outflowregion between the shocks is sometimes called the reconnection layer, and some-times the open low-latitude boundary layer [open LLBL]. The plasma speed inthis open LLBL along the magnetopause, Vout , is given by Eq. 15 to be E/Bn

where Bn is the boundary-normal field in the current sheet. The diffusion regionis often called the X-line and extends out of the plane of the diagram.

If we consider the simplest, symmetric case of steady-state with the Alfvénspeed the same in the inflow regions on the two sides of the boundary [VAin], byconservation energy the inflow energy, dominated by the Poynting flux inflowtowards the current sheet from both the magnetosphere and magnetosheath,equals the outflow, dominated by the kinetic energy of the outflow plasma in theopen LLBL. In addition, the rate of mass inflow must equal the rate of massoutflow, from these relations it is easy to show that:

136

Vout = EBn

≈ 20.5 VAin = 20.5 Bin

(µoρ)0.5 (19)

Thus the outflow velocity Vout is independent of the reconnection rate, E.Figure 2c shows that increasing Bn would increase with the angle of the outflowwedges, a. An increase in reconnection rate would proportionally increase theboundary-normal field, Bn [such that Vout is constant] and thus increase the angle,a. If we have a reconnection pulse, therefore, we would expect the outflow wedgeto increase in width and decrease again in response to the changes in a. Thisproduces the pair of bulges in the open LLBL, one on each side if thereconnection site, containing the enhanced boundary normal field produced bythe pulse, as shown in 2d. This concept was discussed by Southwood et al. [1988]and has here been outlined by treating the system as quasi-steady. In fact figure2d shows the results from a proper analytic theory of time-dependent Petschekreconnection, developed by Biernat et al. [1987] and Semenov et al. [1992],similar features have been reproduced in 2-dimensional MHD simulations byScholer [1988]. In figure 2d there is no reconnection before and after the pulse sothe open LLBL reduces to zero width before and after the pulse: in general therecould be a reduced but non-zero rate between the pulses, in which case the openLLBL is continuous but varies in thickness. Notice that both the sheath andmagnetosphere fields are draped over the bumps in the open LLBL. As the bulgesevolve away from the reconnection site they may pass over a satellite. This wouldcause the field to tip away from, and then towards the Earth in the northernhemisphere. The same bipolar signature in Bn [defined as the field componentalong the outward normal to the boundary] would also be seen on either side ofthe magnetopause. In the southern hemisphere the signatures on either side of theboundary would have the reverse polarity with negative Bn followed by positive,as shown in 2d. Such signatures are indeed observed and are discussed here insection 4.6.

Figures 2c and 2d show two limits of the general behaviour, steady and fullypulsed reconnection. There are a number of features produced by thereconnection in both these limits and by general cases between them. Firstly thereis a boundary-tangential electric field, Et and the boundary-normal magnetic field,Bn. These exist wherever the open field lines convect to from the X-line, butusually cannot be observed directly because of the problems associated with theboundary motions and orientation. However, this certainly does not mean thatthere is no evidence for reconnection in magnetopause observations. Alsoproduced by the reconnection are open field lines which thread the magnetopausevia a rotational discontinuity [RD] in the field and which convect away from thereconnection site. Usually the Alfvén speed [defined in Eq. 19] is greater on the

137

magnetospheric side of the boundary because the field is greater and the plasmadensity ρ is smaller. This means that the field rotation at the shock on themagnetospheric edge of the open LLBL propagates away from the reconnectionX-line faster than does the corresponding kink at the shock which is on the sheathedge. This can be seen to be developing for the field lines further from the X-linein the outflow region in figure 2c. Thus well away from the X-line, the fieldrotation becomes a single RD at the shock on the sheath edge of the LLBL in thiscase [Vasyliunas, 1995]. Magnetosheath plasma is found in the LLBL on theinside of the field reversal, which is often used as the best indicator of themagnetopause. Notice that this assumes a reconnection site which is near the noseof the magnetosphere where the sheath flow is small: away from this region, onthe flanks of the magnetosphere, the increased sheath flow can convect the outerfield kink faster than the inner one, in such cases an open LLBL may be seen onthe outside, not inside, of the magnetic field RD [Lin and Lee, 1994]. In the nextsection we will look at the evidence for RDs in field lines convecting away fromthe reconnection site.

Z

X

BB

Vx

Vx

Vf cos

Vf cos

Vf

VA

i

i

s

s

Pn

o

o

zV zVV

Vmin

Vminp

V

V

=

-- = V +A

=

(a). (b). (c).

Figure 3. (a) The rotational discontinuity (RD) formed by a newly opened field line, threa-ding the magnetopause at Pn and which evolves along the magnetopause in the Z direction atspeed Vf in the Earth’s frame of reference. The X direction is here the outward normal to theboundary. (b) A velocity space plot showing field-aligned bulk flow at the Alfvén speed, VA, inthe de Hoffmann-Teller frame (Vx,Vz with origin at O) both into the RD in the magnetosheath(at s) and away from the RD in the magnetosphere (at i). This geometric construction allowsthe calculation of the minimum (Vmin) and bulk flow (Vp) field-aligned speed of injected parti-cles in the Earth's frame (Vx,Vz) with origin at O'. (c) The truncated, drifting Maxwellian iondistribution function ("Cowley-D") injected at Pn shown in the Earth's frame as a function ofthe field parallel and field perpendicular ion velocities (V|| and V⊥ ^). Between the dashedlines is the part of the distribution for which ions will reach the ionosphere without mirroringin the converging magnetic field lines. [Adapted from Cowley, 1982].

138

4.4. Stress-balance test and accelerated flowsFigure 3a shows the RD formed by an opened field line, convecting away from

the X-line in the z direction, with the x axis here used to denote the outwardnormal to the boundary. This figure is in the de-Hoffman-Teller [dHT] frame ofreference in which the electric field is zero [de Hoffman and Teller, 1950]. If wethink of the field lines moving with the plasma with velocity E × B/B2 [i.e.frozen-in applies] this means that they are at rest in the dHT frame. We can apply(a) Ampère's law [in integral form] to a box in the xz plane which encompassesthe current sheet, along with (b) the balance of forces tangential to the boundaryin the z direction, (c) conservation of mass and (d) the condition that thetangential electric field Et must be continuous across the boundary. It is thenpossible to show that the plasma drifts into and out of the RD along the field linesat the local Alfvén speed [taken here to be the same on the two sides of theboundary, for simplicity] in the dHT frame. This is a general result for an ideal-MHD, time-stationary, RD. If we transform this result into the Earth's frame ofreference, in which the field lines [and the dHT frame] are moving at speed Vf =Et/Bn , we obtain:

V = V f ± B

(µoρ)0.5. (20)

This is called the Whalén relation and can easily be generalised to allow for ananisotropic plasma pressure [a factor not included here for the sake of simplicity][Fuselier et al., 1992]. The plus or minus refers to direction of the boundary-normal field Bn and thus is different on the two sides of the X-line.

Equation 20 is a vector equation and thus applies to any one component [inany direction j]. Tests of this relationship are called the stress-balance test, as Eq.20 is based on the balance of boundary-tangential forces. When Bj is plottedagainst Vj in magnetopause data, a straight line is obtained, as predicted byEq. 20] [Paschmann et al., 1979; 1986; Sonnerup et al., 1981; 1986; Johnstone etal., 1986]. The inferred Vf are typically 150-300 km s-1 and the polarity of Bn

reverses near the magnetic equator, such that field lines enter the magnetospherein the northern hemisphere and leave in the southern, consistent with a low-latitude reconnection site X, as shown in figure 1 [Paschmann, 1984]. Theseresults show that the magnetopause is an ideal-MHD RD [i.e. the field linesthread the magnetopause and are frozen-in to the plasma] - the only exceptionbeing in the small reconnection diffusion region. The open field lines are alsoseen to convect over the magnetopause, away from the reconnection site, atseveral hundred km s-1. The one problematic result is that by Fuselier et al.[1993] who essentially found that ionospheric O+ ions, invoked by Paschmann etal. to be in the LLBL from their stress-balance test results, were largely absent.

139

There are a number of possible explanations for this. When applying the stresstest, it is important to ensure all relevant, and only relevant, particles areincluded: this may not have been possible with the limited temporal resolution ofthe data used by Fuselier et al. It is also possible that the problem is related to theobservations of ion temperature rises in accelerated flow regions, which wouldnot be expected for an ideal-MHD RD magnetopause [Paschmann, 1984].

Z

YX

IMF

X

YY

X

ZZ

open

closed

IMF

R2

R1 R1

C

(c).

(a). (b).

(d).

Figure 4. (a). The antisunward transfer of open flux produced by reconnection and of closedflux, due to non-reconnection or "viscous-like" interactions on closed field lines on the flanksof the magnetopause. (b) and (c). The origins of asymetric dayside flows and currents in thedayside magnetosphere-ionosphere system (the Svalgaard-Mansurov effect). Open field linesare shown shortly after they were formed by reconnection with an IMF that points southward(Bz < 0) and towards dusk (By > 0). The vectors show the "tension" forces resulting from thecurvature of these newly-opened flux tubes. In both hemispheres, this force has a polewardcomponent: in the northern hemisphere it also has a dawnward component (i.e. in the nega-tive Y direction), whereas there is a duskward component in the southern hemisphere. (d)shows the resulting flow streamlines (solid lines and arrows), Pedersen currents (dashedlines and open arrows) and field aligned currents (into and out of plane of diagram) in theionosphere: noon is to the top, dusk to the left and dawn to the right. The field-aligned cur-rents are divided into Region 1 (R1), Region 2 (R2) and Cusp (C). The sense of dawn-duskforces in (b) and (c), of the consequent dawn-dusk asymmetries in flows and Pedersen cur-rents near noon in (d) and of the polarity of the cusp field-aligned currents are all reversedwhen IMF By < 0.

Consider the magnetosheath plasma flowing into the magnetosphere. Infigure 3 the sheath ions incident on the magnetopause are marked s and thoseinjected across the magnetopause into the open LLBL are marked i. Figure 3b is a

140

velocity space diagram, with O being the origin of the dHT frame and O′ theorigin in the Earth’s frame. The incident sheath ions in 3a are moving in the -z and-x directions, i.e. Vx < 0 and Vz < 0 in the dHT frame. The bulk flow speed is thelocal Alfvén speed VA in this frame and this flow is at the point s in both 3a and3b. After crossing the RD, the injected ions (i) are moving with Vx < 0 and Vz > 0.As the bulk flow ion speed is still VA in the dHT frame, i must lie on the dashedcircle radius VA , centred on O, as shown in 3b. In the Earth's frame, the crossingof the magnetopause [i.e. from s to i] corresponds to a large acceleration [ofalmost 2VA on the dayside where θ and φ are sufficiently close to zero that cosθ ≈cosφ ≈ 1].

Accelerated flows are indeed seen at the dayside magnetopause [e.g. Smith andRodgers, 1992; Scurry et al., 1994]. Their speed satisfies the stress balance testdescribed above. In addition their direction is as predicted by the reconnectionmodel. This is explained by figure 4b which is a view of the daysidemagnetosphere from mid-latitudes and mid-afternoon. The same situation isviewed from the sun in figure 4c.

The diagrams show newly-opened field lines produced by reconnection at asubsolar magnetopause for a southward IMF which points toward dusk [By > 0].The vectors show the curvature force on the kink in the newly opened field lineswith components in the poleward and dawn-dusk directions. For this case, thezonal force [and resulting field line and frozen-in plasma velocity] is in the -Ydirection in the northern hemisphere and in the +Y direction in the southern.These zonal directions are reversed when IMF By < 0. The observations byGosling et al. [1990a] show that the direction of the accelerated flows depends onBy as expected from figure 3.

An important point is that once field lines are open, plasma streams across theboundary along the open field line at all stages in its evolution, until it is re-closed by reconnection in the tail [at Xt in figure 1]. This has been confirmed bythe stress balance test, not only on the dayside magnetopause, as described above,but also at the near-Earth tail boundary [Sanchez et al., 1990; Sanchez andSiscoe, 1990] and recently by observations by the Geotail satellite in the far tail[Siscoe et al., 1994]. However, the characteristics of the injected plasma changeas the field line evolves. Figure 3 shows the RD for a newly-opened field linethreading the dayside magnetopause, with the angles θ and φ being small. Thisacute-angle RD in the field corresponds to Chapman-Ferraro currents out of theplane of the diagram, as can be seen in figure 1. Note that for this daysidemagnetopause J and E point in the same direction, i.e. J . E > 0. However, as thefield line evolves, the angles θ and φ both increase and (θ+φ) exceeds π. For thisobtuse-angle RD, the equivalent construction to figure 3b shows the ions are

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decelerated, not accelerated, on crossing the boundary. The correspondingChapman-Ferraro current is here into the plane of the diagram, i.e. J . E < 0 [seefigure 1] [Hill, 1979]. Note that in the tail lobe boundary, the field line velocity,Vf, is away from the Earth, whereas it is toward it on the dayside. Because theflow is super-thermal, very little of the ion distribution injected across the taillobe magnetopause [the high-latitude boundary layer, HLBL] will have a velocitytoward the Earth and will precipitate to the ionosphere. Those that do [the hot tailof the population in the dHT frame] will form a low-energy [in the Earth’sframe], low-density precipitation in the polar cap. This contrasts with ions in theopen LLBL on the dayside which are accelerated toward the Earth and precipitatein the "cusp" region. Electrons precipitate with roughly equal fluxes to the ions,in such a way as to maintain quasi-neutrality of the plasma [Burch, 1985].

During northward IMF, accelerated flows are still observed, but in such casesthey are streaming away from a reconnection site at high latitudes on the daysideedge of the tail lobe HLBL [Gosling et al., 1991; Paschmann et al., 1990]. Asurvey of accelerated flow directions by Scurry et al. [1994] has confirmed thatthey emanate from a low-latitude reconnection site during southward IMF, butfrom a tail lobe site during northward IMF.

4.5. Particle populationsThe previous section described how the bulk flow of the plasma into and away

from the ideal MHD RD that is the magnetopause [away from the X-line]. Aboutthis bulk flow velocity there will be a thermal spread of speeds. One hot tail ofthe distribution of incoming sheath ions will have field-aligned flow speeds, V||

which are away from the boundary. They will thus fail to cross the boundary.Ions with V|| = 0 will just manage to cross the boundary and in the Earth’s frame

will be accelerated to [Vf cos θ]. Hence this will be the minimum field-parallelvelocity Vmin of the injected sheath population; Cowley [1992] used sucharguments to predict the D-shaped distribution function of the injected sheathpopulation, as shown in figure 3c. To make his predictions, he noted that therewere three populations incident on the magnetopause, the sheath population fromthe outside and the ionospheric and ring current populations from the inside.Each of these populations will be scattered at the current sheet and some will bereflected by the boundary and some will be transmitted through it. Cowleyassumed that in either case the pitch angle of the ion was conserved oninteraction with the boundary. This is clearly not a good assumption whendealing with individual particles, but when dealing with a statistical ensemble thescattering does not alter the form of the distribution functions. The injectedpopulation in figure 3c is a truncated drifting Maxwellian, often referred to as a"Cowley - D" distribution.

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Almost ten years after these predictions were made, they were verified inobservations of accelerated flows at the dayside magnetopause [Gosling et al.,1990b; Smith and Rodgers, 1991; Fuselier et al., 1991]. In addition to showingthe D-shaped distribution functions of the accelerated injected ion flows in theopen LLBL, Smith and Rodgers applied the stress-balance test and showed thatthe cut-off was at the velocity Vmin ≈ Vf [for close to the X-line θ ≈ 0], aspredicted by the theory. In addition, Fuselier et al. studied He+ and He++ ionsbecause these are known to be of magnetospheric and magnetosheath origin,respectively. They found not only the injected sheath ions, but all populations[incident, transmitted and reflected] were as predicted by Cowley, on both sidesof the boundary. The distributions have also been reproduced in simulations byLin and Lee [1993].

In figure 3c there are two dashed lines at fixed pitch angle. Ions between thesetwo lines are the only ones with a sufficiently field-aligned velocity vector toprecipitate into the ionosphere without first mirroring in the converging magneticfield lines. This precipitation is discussed further in section 6.3. Lastly, we notethat electrons do undergo a corresponding dHT acceleration on crossing themagnetopause, but the increase in speed is negligible compared to the speed withwhich they approach the magnetopause. [For example, an electron with the sameenergy as an ion will have a greater speed by a factor of (mi / me )½~ 40].

4.6. Flux Transfer EventsAs discussed in section 4.3, a pulse of enhanced reconnection rate is expected

to cause a pair of bipolar signatures in the boundary-normal field, Bn, whichmove away from the reconnection site at the field line velocity, Vf. Suchsignatures have been known for over a decade and are termed flux transfer events[FTEs], first reported by Russell and Elphic [1978] and Haerendel et al. [1978].The name originates from the interpretation because, as discussed earlier, a burstof enhanced reconnection rate, when integrated along the X-line, is a voltageburst which is synonymous with the term "flux transfer event". By definition, theflux is transferred from the closed to the open region by the reconnection, but it isseen some time later as it is transferred into the tail lobe under the action of themagnetic curvature force and the magnetosheath flow. This interpretation ofFTEs predicts that their polarity reverses sense across the X-line, a feature whichis found in experimental data if we infer the X-line to be at low latitudes on thedayside magnetopause [Berchem and Russell, 1984; Rijnbeek et al., 1984]. Thesestatistical surveys also show that the events are almost exclusively a southwardIMF phenomenon and repeat every 7 minutes on average. It should be stressedthat this is an average value of what Lockwood and Wild [1993] find to be ahighly skewed distribution, with a mode repeat time of 2-3 min. The dependenceof the occurrence of FTEs on IMF Bz strongly implicates the reconnection

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process, as do particle observations of the plasma in the centre of an FTE whichreveal a mixture of sheath and magnetosphere plasma [Thomsen et al., 1987], asexpected for newly-opened flux along which plasma from both sides can flowacross the boundary and mix, as described in the previous section. The FTEmodel presented in figure 2d is slightly different from that presented by Russelland Elphic, although very similar in basic concept. The main difference is thatRussell and Elphic used a circular newly-opened flux tube whereas figure 2d is 2-dimensional and events are not defined in their extent out of the plane of thediagram. Not all scientists have agreed with this interpretation of magnetopauseFTE signatures as resulting from reconnection bursts. In particular, Sibeck [1992]has used a conceptual argument that they are caused by magnetopause surfacewaves driven by solar wind dynamic pressure pulses. However, there are anumber of problems with this interpretation, for example: the postulated pressurechanges are not found in the sheath [Elphic et al., 1994]; the boundary thickensrather than thins in an event [Hapgood and Lockwood, 1995]; the occurrencestatistics with IMF Bz is not well reproduced; and there has been much debate asto if the pressure-pulse mechanism would really produce FTE-like signatures[Lockwood, 1991; Song et al., 1994]. It seems that the original concept of FTEs isvalid, however, Sibeck’s work has highlighted the need for careful identificationof FTEs as they are not the only cause of fluctuations in Bn.

5. Transfer of energy, mass and momentum from themagnetopause to the ionosphere

5.1. Poynting’s theoremIf we compress a magnetic field by dτ in volume, we do work against the

magnetic pressure which, by Eq. 18 is ∂WB = (B2/2µo)dτ. Thus the rate at which

energy is stored in the field in a volume τ is:

∂WB

∂ t = ∂∂ t

⌡⌠

τ

B2

2µo dτ =

1µo

⌡⌠

τ

(B . ∂B/∂ t ) dτ

If we substitute from Faraday’s law Eq. 10, use the vector relation (E × B) = B . ( × E) - E . ( × B), Ampère's law Eq. 9, the divergencetheorem and the definition of Poynting flux S = (E ×€B)/µo, we get Poynting'stheorem:

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∂WB/∂t = - ⌡⌠

A

S . ds -

⌡⌠

τ

E . J dτ (21)

where the surface S surrounds the volume τ. The first term on the right is thedivergence of the Poynting flux and the second is the ohmic heating term. If weuse Ohm’s law Eq. 7, we can show that the heating term has two parts:

B

AB

C D

E

E

S Sv

E Jp

JCF

B

F = J xBp

v =ExB/B

2

B

J =

J =

A

B

C

D

Jp

JCF

E

E

tail magnetopause, J.E < 0

ionosphere, J.E > 0

(a). (b).

Figure 5. The role of field-aligned currents J|| in the transfer of energy and momentum fromthe magnetopause to the ionosphere.(a) shows an ideal matched pair of filamentary field-aligned currents which form a circuit with the Chapman-Ferraro currents (JCF) in the tailmagnetopause and the Pedersen currents (Jp) in the ionosphere. The field-aligned currentscause a field perturbation,B, which tilts the field lines with respect to their orientation inthe absence of the currents, as shown in (b). The electric field E applied by the solar windflow is oppositely directed to the Chapman-Ferraro currents, making J . E < 0 so that thisportion of the magnetopause is a source of Poynting flux, S=E x B (see figure 1). Conversely,the Pedersen currents are in the same direction as E, i.e. J . E > 0 and the ionosphere is asink of Poynting flux. Thus energy is extracted from the magnetosheath flow at the tail ma-gnetopause and is deposited in the ionosphere. The tilting of the field lines produces a down-ward component of the Poynting flux, Sv, which transfers the energy from the magnetopauseto the ionosphere. The motion of the ionospheric plasma at the velocity v = (E x B)/B2 isopposed by the frictional drag caused by the neutral atmosphere and is maintained by the J xB force associated with the Pedersen currents. These concepts are sometimes referred to as"line-tying".

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⌡⌠

τ

E . J dτ =

⌡⌠

τ

J 2

σ dτ - ⌡⌠

τ

V . ( J × B) dτ (22)

where the first term on the RHS is the resistive energy dissipation and the secondis the mechanical work done against the J × B force.

If we consider steady state, ∂W/∂t is zero and a region where J . E > 0 is a sink ofPoynting flux, i.e. energy goes from the electromagnetic field into the particles.Conversely regions of J . E < 0 are sinks of Poynting flux, i.e. energy goes fromthe particles into the electromagnetic field. The dashed lines in figure 1 show thePoynting flux and how the dayside magnetopause is a sink of S, whereas the taillobe boundary is a source. This means that energy is extracted from the solarwind flow at the tail lobe boundary [HLBL], but put into the accelerated ions onthe dayside LLBL.

If we have no Ohmic heating [J . E = 0] with non-steady state, a region ofincreasing magnetic field will be a sink of Poynting flux and conversely a regionof decreasing field will be a source. An example of the former is the tail lobesduring the growth phase of a substorm: energy is then stored in the lobe and it is asink of the Poynting flux generated at the HLBL magnetopause [as can be seen infigure 1]. In the later phases of substorms, the lobe field decreases again, so thelobe becomes a source of Poynting flux which takes the stored energy anddeposits in the tail plasma sheet, the ring current and the ionosphere. Thus thelobe acts as a store for the extracted energy which is later released in substorms.

5.2. The role of field-aligned currentsFigure 5 shows how field aligned currents can transfer the solar wind

momentum and energy into the ionosphere [see Southwood, 1987]. The figureshows an idealised pair of straight field-aligned filamentary currents which closethrough an element of Chapman-Ferraro current at the magnetopause and a linearPedersen current in the ionosphere. [In reality, the Pedersen current will spreadout over an extended region around the field-aligned current filaments,corresponding to the "return" flows required outside the filaments because theionosphere is incompressible]. These field-aligned currents [J||] cause a

perturbation to the magnetic field B, as shown. We show a segment of the tailmagnetopause where J CF. E < 0, which is a source of S [figure 1] and, bydefinition J P. E > 0 which is a sink of S. Figure 5b shows the plane ABCD

between the filamentary field-aligned currents [see 5a]. The perturbation Bcauses a tip in the field lines. In the ionosphere, the field line moves horizontallybecause of the JP × B force which is opposed by the frictional drag on the

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ionospheric plasma caused by collisions with the neutral gas. In steady-statethese forces are balanced and the field lines move with constant speedcorresponding to the E × B/B2. If we consider the magnetic flux F threading thecurrent loop shown in 5a, by Faraday’s law Eq. 16, the rate of change of F is theintegral of E . dl around the loop. If we assume frozen-in applies [to a goodapproximation] E|| is zero and so we have

O⌡⌠

E . dl = Et dlm - Ei dli =

∂ F∂ t (23)

where Et and Ei are the magnetopause and ionosphere electric fields and a lengthdlm maps to a length dli in the ionosphere. The RHS of Eq. 23 is zero in steadystate and thus, Ei= Et (dlm/ dli), we speak of the electric field mapping down fieldlines or, equivalently, the magnetopause voltage being equal to the voltage acrossthe ionospheric footprint. [In the simplified picture given in figure 5, dlm = dliand so the electric field is everywhere the same in this steady state limit]. Figure5b also shows the Poynting flux, S, which because of the tilt of the field lines hasa downward component, Sv, which connects the source at the magnetopause withthe sink in the ionosphere.

Figure 5 therefore demonstrates how field-aligned currents transfer bothelectromagnetic energy and momentum from the magnetopause to the ionosphere.The concepts embodied in this figure are often referred to as "line-tying". Itshould be noted that the frictional drag in the ionosphere makes it difficult tomove, but that current systems in the magnetosphere may change more rapidly,allowing field lines to bend, altering ∆B at any one location and its integral overthe loop, F. From Eq. 23, the electric fields will then no-longer map from themagnetopause to the ionosphere. In terms of an electrical circuit analogy, theionosphere is a resistor and the magnetosphere acts as an inductance. Thus intime-varying situations, the ionosphere will be slow to respond to a change in thetangential magnetopause electric field and the field-aligned currents will changeon the inductive time constant of that response. For a single, step-function changein the magnetopause electric field, the ionospheric flows and the correspondingfield aligned currents will rise asymptotically towards the steady-state value, withthe inductive time constant. If the magnetopause electric field fluctuates then theionospheric flows and the field aligned currents will, in general, show thesefluctuations, but they will be inductively smoothed to a degree which depends onthe ratio of the fluctuation period to the inductive smoothing time constant. Froma variety of studies, we find the inductive time constant for the dayside to be oforder 10-20 min. This has been estimated from electrical circuit analogies [Holzer

147

and Reid, 1975; Sanchez et al., 1991], from line-tying arguments [Coroniti andKennel, 1973] and measured directly from the response of dayside ionosphericflows and currents to southward and northward turnings of the IMF [Nishida,1968; Etemadi et al., 1988; Todd et al., 1988; Hairston and Heelis, 1995].

Time-dependent situations will be discussed further in section 7.

5.3. Directly-driven ionospheric convectionFigure 4a illustrates the two ways in which magnetospheric convection can be

driven. The diagram shows a newly-opened field line convecting away from asubsolar reconnection site. Initially this motion is due to the curvature ["tension"]force, but as it straightens the magnetosheath flow becomes more important. Theother flux tube shown remains closed and is convected into the tail by some formof momentum transfer across a tangential discontinuity [TD] magnetopause.Because this applies to all mechanisms, other than reconnection, they are groupedtogether under the term "viscous-like interaction". The nature of that interactionwill not be discussed here, other than to mention that possible, valid and viablemechanisms include the Kelvin-Helmholtz instability, wave-driven diffusion, andfield-aligned current generation by compressive magnetopause motions producedby solar wind buffeting. For either an open or a closed field line, the antisunwardmotion will, in steady-state, be communicated to the ionosphere by field-alignedcurrents, as discussed in relation to figure 5. The results are shown in figure 4d

which is a view of the northern hemisphere polar cap, with noon at the top anddawn to the right. [Note there is a deliberate dawn-dusk asymmetry in this plotwhich will be discussed in the next section]. The solid lines with arrows are flowstreamlines in the F-region and topside ionosphere, which do not cross or touchbecause the ionosphere is incompressible. The dashed lines with open arrowsshow the E-region Pedersen currents. As these are parallel to the applied electricfield they are everywhere normal to the F-region flow which is a frozen-in (E ×B)/B2 drift. The Pedersen currents are closed by field-aligned currents, shown assymbols into and out of the plane of the diagram. The dashed line across noon isthe ionospheric projection of the reconnection X-line shown in 4a, other [non-reconnecting] parts of the open-closed boundary are shown as solid lines [nearerdawn and dusk]. These non-reconnecting segments are called "adiaroic" [fromthe Greek and meaning "not flowing across"] [Siscoe and Huang, 1895].Magnetopause reconnection, by definition, is the transfer of flux from closed toopen. In this steady-state case, the open-closed boundary [dashed line] is still andflow streamlines crossing this boundary are driven by reconnection at that localtime [note that this is not necessarily the case in the time-varying situationsdiscussed in section 7]. The viscous-like momentum transfer is seen on the flowstreamlines on the flanks of the open field line region where the sunward flowturns antisunward. The flows change direction at a convection reversal boundary

148

[CRB] which lies equatorward of the open-closed boundary [OCB]. The field-aligned currents at the CRB are down near at dawn and up near dusk and arecalled the region 1 [R1] currents, a name commendably free of the theory of theirorigin [Iijima and Potemra, 1976]. These must close in the Chapman-Ferrarocurrents, but first have to traverse the closed LLBL, between them and the open-closed boundary [Siscoe et al., 1991] [N.B. this cross-closed LLBL current isthought to give the J×B force which balances the weak viscous forcing on theclosed LLBL field lines, Lotko et al., 1987]]. The antisunward flow poleward ofthe CRB must be matched by sunward flux transport equatorward of it, becausethe ionosphere is incompressible. This sunward transfer is confined to a relativelynarrow band at auroral and sub-auroral latitudes by a second set of field-alignedcurrents, called the region 2 [R2], which close in the ring current, which have theopposite sense to the region 1 currents at the same local time. The double-annulusof field-aligned currents was discovered by Iijima and Potemra [1976].

The rate of flux transfer [i.e. voltage] between the dawn and dusk CRBs can bemeasured by satellites which fly across the polar cap at low altitudes, byintegrating the observed electric field [often taken from the ion drift using Eq. 14]along the satellite orbit. This is often referred to as the "cross-cap potential" but isactually a potential difference [i.e. a voltage] and so I prefer the name transpolarvoltage, Φpc. The observations show that Φpc increases with increasinglysouthward IMF [Reiff et al., 1981; Cowley, 1984] up to values of over 100 kV.This is in accordance with expectations for the reconnection momentum transfer,as the reconnection process requires the antiparallel fields, and the maximummagnetic shear is when the IMF points due south. Curiously, this is wellreproduced by global MHD models, which assume the frozen-in condition appliesat all locations! [e.g. Fedder et al., 1991]. This arises because the models makeerrors in tracing field lines and accidentally connect geomagnetic field lines withinterplanetary ones to produce open field lines. The rate at which this happens isnot dependent on the model grid size and mimics the reconnection behaviour inthe real magnetosphere because the equations for the propagation of thisnumerical error are very like the diffusion term in the induction Eq. 11.

When the IMF is northward, the only expected antisunward flux transfer is thatdue to viscous interaction and the physically-meaningful mechanisms for viscous-like interaction predict no dependence on the orientation of the IMF. Thus thelow values of Φpc under Bz > 0 conditions [< 30 kV] put a limit to the importance

of viscous-like interactions. In fact Φpc gradually decreases to even lower valueswith increasing time since the IMF turned northward, implying that much of theresidual voltage is in fact driven by continuing reconnection in the tail [Xt infigure 1] [Wygant et al., 1983]. Fox et al. [1994] have shown how the ionosphericflow pattern can mimic viscous interaction processes as the polar cap contracts.They also found that the apparently-viscous voltage is enhanced when

149

the polar cap is contracting more rapidly, showing it is actually associated withthe reconnection at Xt which caused the contraction. Thus the true level of viscousinteraction voltage is the 5-10 kV observed several hours after a northwardturning, when both the dayside and the tail X-lines [X and Xt in figure 1] areinactive. Note that viscously-driven voltages should be the same in bothhemispheres, and the voltage on either flank should be matched in the twohemispheres.

The transpolar voltage [sunward flux transfer] when the IMF is northward [Freeman et al., 1993]. Thisshows sunward or "reverse" convection and is primarily a phenomenon of thesummer hemisphere polar cap [Crooker and Rich, 1993]. This is caused byreconnection at high latitudes between the magnetosheath field and the already-open flux of the tail lobe, and will discussed in section 5.5.

A second indication of the relative roles of reconnection and viscous-likeprocesses is obtained by noting that the open field lines are transportedantisunward out of the equatorial [XY] plane, whereas the antisunward transportof closed field lines will be seen in the equatorial plane as well as in theionosphere. Observations of the voltage associated with anti-sunward fluxtransfer in the flanks of the magnetopause show it is small, typically <10 kV[Mozer, 1984]. These observations are, however, very difficult to make becausethe boundary motions will alter the amount of time that the satellite spends in theLLBL and the electric field is measured in the satellite ’s frame and will bedifferent in the moving frame of the boundary. However, this effect should causeboth overestimation and underestimation of the voltage. Furthermore, boundarymotions can be measured and accounted for with multiple craft and the voltagehas been shown to be small in such cases [< 5 kV] similar to values deduced from Lockwood, 1995].

These observations show that reconnection is the dominant mechanism for thedirect driving of magnetosphere-ionosphere convection, and the associated field-aligned currents.

5.4. The Svalgaard-Mansurov effectAs discussed in relation to figure 4b, low-latitude reconnection of the

geomagnetic field with an IMF which has a large By leads to a motion of fluxtubes in the ±Y direction, under the influence of the magnetic curvature force.

150

c

ov v

1

345

2

c

X

MP

2

1

3 4 5

o

reconnecting segment ofopen (o) - closed (c)boundary (merging gap)

non-reconnecting segment ofo - c boundary (adiaroic)

i

i = interplanetary field lines; v = viscous - driven flows

(a). (b).

Z

X Y

Figure 6. Schematic of the motion of newly-opened field lines away from a low-latitude re-connection site, X, when the IMF points southward. (a). Shows an noon-midnight sectionthrough the dayside magnetosphere, viewed from dusk and with the magnetopause as thedotted line MP. The field line 1 is closed (c), prior to being opened at X by reconnection withthe draped interplanetary field line in the magnetosheath, i. Field lines 2-5 are open (o) fieldlines at different points in their subsequent evolution into the tail lobe. (b) shows the corres-ponding ionospheric flow streamlines in both hemispheres for steady-state conditions, thenumbered dots being the locations of the field lines shown in (a): noon is at the top of thefigure, dusk to the left and dawn to the right. The boundary between open and closed fieldlines is shown as a dashed line where it maps to the X-line (the "merging gap"), but as a solidline where it maps to a non-reconnecting segment of the magnetopause. The flows marked vare driven by viscous-like interactions between the magnetosheath flow and closed field lines.

This motion is communicated to the ionosphere [by field aligned currents] andthis gives east or west flow, depending on the sense of By and the hemisphere inquestion. This effect was graphically illustrated by Greenwald et al. [1990] usingconjugate radars to view the cusp regions in both hemispheres simultaneously.The effect was first noted in the E-region currents which correspond to theseflows and is termed the Svalgaard-Mansurov effect after the scientists involved[see review by Cowley, 1981a]. In addition to the antisunward and sunwardconvection [and associated R1 and R2 field-aligned currents] discussed in the lastsection, figure 4d also shows the northern hemisphere flows [and associated R1/Cfield-aligned currents] corresponding to the By > 0 case presented in figures 4band 4c [after Cowley et al., 1991b]. Westward flow is found on the straighteningnewly-opened field lines, immediately poleward of the open/closed boundary[OCB, shown as a dashed line] around noon. The momentum is transferred to theionosphere by the field-aligned currents on the poleward and equatorwardboundaries [C and noon R1, respectively] of this region [cf. figure 5]. The equa-torward part of this pair lies near the open-closed boundary and so is generallytaken to be part of the region 1 ring. The poleward part lies on open

151

field lines and is called the cusp or mantle currents. The origin of these currents atthe magnetopause, in terms of the unbending of the kinked newly-opened fieldlines was discussed by Saunders [1989] and Mei et al. [1995].

5.5. Convection for southward and northward IMFFigure 6a shows a view from dusk of a newly-opened field line evolving away

from a dayside reconnection site, X, during southward IMF. The positions of thefield line are shown at times 1-5 [in steady state this is also a snapshot showingthe simultaneous positions of 5 different field lines]. In position 1 the field line isclosed [c] but in 2-5 it is open [o]. The reconnection site has deliberately beenplaced away from the geomagnetic equator to stress the precise location at whichthe field line is opened does not matter - other than the X-line must be betweenthe two magnetic cusps to open closed flux [this is what is here meant by a "low-latitude" X-line]. Figure 6b is a simplified version of figure 4d for IMF By ~ 0,which shows the corresponding locations of that field line in the F-regionionosphere. The flow is steady state and streamlines only cross the open-closedboundary at the ionospheric projection of X [the dashed line]. The viscously-driven cells are labelled v.

Figure 7a shows one of the possible corresponding situations during northwardIMF. In this case, the reconnection site X is at the front edge of one tail lobe [herethe northern hemisphere lobe] and the reconnection takes place between alreadyopen field lines in the lobe and the draped sheath field lines. Figure 7b shows thenorthern hemisphere ionosphere. The open-closed boundary is everywhereadiaroic as no low-latitude reconnection is taking place. The projection of X [thedashed line] is poleward of this boundary. The numbers show the evolution of anopen field line, which remains open after reconnection at X, but such that itthreads the boundary near the Earth, instead of at a large distance down the tail.This field line is then moved around the [in this case] dawn flank, under thecompeting influences of magnetic tension and sheath flow, and eventually wouldreturn to be reconfigured again at X [if the reconnection remains active for longerthan the circulation time]. Thus this produces a circulation flow cell in the lobe.Figure 7b is for IMF By ~ 0 and shows two symmetrical lobe cells [L] withreconfigured field lines passing to both the dawn and dusk sides. The other[southern] hemisphere lobe is not subject to this effect and would be stagnantother than for the viscous flow cells. This situation has recently been reported inobservations for extended periods of time when the IMF is northward [Freemanet al., 1993].

152

1

345

6

2

o

L L

c

v v

1

3

4

5

6

2

c

X

MP

o

projection of lobereconnection X-line

non-reconnecting open (o)-closed (c) boundary (adiaroic)

ii

i = interplanetary field linev = viscously-driven flowL = lobe flow cell

(a). (b).

Figure 7. The same as figure 6, but for a steady-state case with reconnection at a northern-hemisphere lobe site, X, during northward IMF. In (a), the field lines 1 and 2 were openedduring a prior period of southward IMF and have remained open: they are seen convectingtowards X, where they are reconfigured (such that the point where they thread the magneto-pause is moved from the far tail to immediately sunward of X). Field lines 3-6 show the evo-lution of these reconfigured open field lines around the dusk flank of the Earth (in this case)forming a circulation in the polar cap. For the case of small By component of the IMF, thereis a corresponding circulation on the dawn flank, and two symmetrical flow cells in the io-nospheric polar cap ("lobe cells", L) as shown in (b). These sit poleward of any viscously-driven cells, forming a four-cell pattern. In cases of large |By| (not shown) one of the lobeflow cells will dominate, giving a three-cell pattern with a single circulation cell in the polarcap in the sense determined by the polarity of By.

Figure 7 therefore is consistent with the observations of large negative discussed in section 5.3, that voltage being between the centres of the two lobecells. These are surrounded by the viscous cells giving a four-cell form of theoverall convection. Figure 7 is also consistent with the observations ofaccelerated flows away from a lobe reconnection site by Gosling et al. [1991],and with the observations of accelerated flows towards the equator at lowlatitudes by Paschmann et al. [1990]. The latter are on field lines like 3 in figure7 which are now often referred to as an "overdraped lobe" [Crooker, 1992].

Figure 8 considers a second situation which can occur during northward IMF.In this case, the overdraped lobe field lines [ol] are reconnected at a second X-lineX1 that is in the opposite hemisphere to X. This second reconnection re-closes theoverdraped-lobe field lines, like 2 and 3, producing the closed field line 4. Afour-cell flow pattern again results [figure 8b], but unlike the case in figure 7, the

open/closed boundary is not all adiaroic, there is a merging gap [dashed line],with the opposite polarity voltage to that seen in the southward IMF case [i.e. adusk-to-dawn electric field]. In this case, the southern hemisphere would alsoshow a four-cell pattern with sunward flow in the central polar cap as the

153

open field lines are reconnected at X1. The principle difference from figure 8b isthat in the southern hemisphere there would be no projection of X.

A special case of figure 8 is when the same field line is simultaneously recon-nected at X and X1, i.e. the two X-lines have the same footprint in both hemi-spheres. This is the original topology envisaged by Dungey [1963] when he firstconsidered the northward IMF case. However, it requires a considerable co-incidence for this to happen and the general case shown in figure 8 is much morelikely [Russell, 1972] [note, however, X and X1 could swap hemispheres].

c

o

1

3 42

ol

v v

13

3

4

4

2

c

XX

X1

X1

MP

o

projection of X-lines X and X1(merging gaps)

adiaroic segment of open (o) -closed (c) boundary

ol

o

i i

c

ii

i = interplanetary field line; ol = overdrapedlobe field lines (here in northern hemisphereonly); v = viscously-driven flow

(a). (b).

Figure 8. Same as figure 7 for a case when lobe reconnection occurs in both hemispheres (atX and X1). The reconnection site X produces "overdraped lobe" (ol) field lines (2 and 3),which are subsequently closed at X1 to give (4).

The topologies shown in figures 7 and 8 are not mutually exclusive. It is possi-ble that X may be more extensive than X1 and some overdraped field lines will bere-closed in the other hemisphere [as in figure 8] while others circulate aroundthe dawn or dusk flank without further reconnection, as in figure 7. In addition,figures 7 and 8 are far from the only topologies possible for northward IMF, andthe reader is referred to Cowley [1981b] and Crooker [1992] for further discus-sion. If the IMF |By| is large, one lobe cell dominates and the flow pattern be-comes three-celled [as in figure 12b] [Heelis, 1984].

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6. The cuspThe previous sections have dealt with the momentum and electromagnetic

energy transfer from the solar wind to the magnetosphere and dayside ionosphere.In this section we look at the mass transfer, which is also associated with someenergy transfer in the form of the kinetic energy of the precipitating particles.This has been left until this section because the convection described in theprevious section is a crucial factor in the precipitation characteristics, because ofthe velocity filter effect.

6.1. The velocity filter effectIn order to illustrate this effect and study its implications, it is valuable to again

make magnetospheric field line straight and parallel [as in figure 5] [Onsager,1994]. Generalisation for the real magnetospheric magnetic field is straightfor-ward if we formulate the description of precipitation to ionospheric heights interms of speeds and distances in the ionosphere and the time-elapsed sincereconnection. This also has the great advantage of making it easy to generalise fornon-steady-state situations [Lockwood and Smith, 1994; Lockwood, 1995a][section 7]. This idealised magnetosphere is presented in figure 9, in both parts ofwhich the magnetopause is on the left and the ionosphere on the right. Themagnetospheric field lines are all horizontal and the field-aligned distance fromthe magnetopause to the ionosphere is d at all times. A uniform convectionelectric field is applied everywhere out of the diagram, so that flux tubes convecttoward the top of the page at speed Vc. We will here be concerned mainly with

precipitation into the ionosphere and, because the real magnetospheric fieldconverges with decreasing altitude, there is a mirror force which acts on particleswith a gyratory motion [i.e. with a pitch angles greater than zero] and reflectsthem back into the magnetosphere. The only particles which reach the ionospherestart with pitch angles close to zero, i.e. their motion is field aligned. We thereforehere consider only zero pitch angle particles, which have a velocity Vi which is

field parallel and an energy ei = (mivi2)/2. Once injected across the magnetopause

[and in the case of ions significantly accelerated] the particles are assumed toundergo adiabatic and scatter-free motion, which means that ei and Vi remain

constant. The distribution function f(ei) also remains constant under thesecircumstances, by what is known as Liouville’s theorem. Thus the time-of-flight i = d/vi. If we consider a

magnetopause source point P as shown in figure 9a, the field line onto which the

particles are frozen will have moved a distance dc from P by the time the particlesarrive at the ionosphere, where

155

P1

P

C

2

B

V

E

c

d

dd

d

i

c1c2

e

P

B

V

E

d

dv

Vi

cc

c

IE

OCBEE

e

e

e

e

im

im

ic

em

(a). (b).

Figure 9. Schematic explanation of the velocity filter effect. Magnetospheric field lines areconsidered straight, over the distance d between the magnetopause on the left and the io-nosphere on the right. A uniform convection electric field is applied out of the plane of thediagrams, causing the field lines and the frozen-in plasma to drift up the page at speed Vc. (a)shows the distance dc that an ion of field-aligned velocity Vi is convected during its time-offlight along the distance d. (b) shows such trajectories for the maximum energy electrons andions (eem and eim) from P1, forming the electron and ion edges (EE and IE, respectively). Theshaded part of the magnetopause is an extended source region, as generated by opening fieldlines by reconnection at P1 (i.e. the field line through P1 is the open-closed boundary, OCB).At C a range of ion energies is seen between eic and eim, corresponding to the range of sourcelocations between P1 and P2

dc = τi Vc = d Vc

vi = d Vc

mi

2ei

½ (24)

Thus the position where a particle from P participates into the ionosphere de-pends on its energy ei. If we inject a full spectrum of energies ei at one point Pthey are spread out according to Eq. 24 and we will only see ions [of one species]with one energy at any one point in the ionosphere [i.e. the ionospheric spectrumfor a point source is a delta function, irrespective of the spectrum injected at P].Different species are seen with energies in proportion to their masses. The energydetected in the ionosphere falls with increasing dc and this dispersion is what wecall the velocity filter effect. In the cusp we see both the convection velocity Vc

and the energy-position dispersion showing the velocity filter effect [Rosenbaueret al., 1975; Shelley et al., 1976; Reiff et al., 1977]. However, we also see a rangeof ion energies at any one point and that shows that the source is not a point.Reconnection provides the ideal way of producing this extended source regionbecause once a field line is opened the plasma streams continuously across

156

the boundary. A complication, however, is that the injected particle populationchanges with position and J . E , as discussed in section 4.5. Figure 9b illustratesthe extended source generated by reconnection, shaded black. The leading edgeof the source region, P1 , is the reconnection site and the field line through thispoint is the magnetic separatrix or open-closed field line boundary [OCB]. Thepoint P2 is downstream of the X-line such that each newly-opened field lineproduced at P1 threads the boundary at P2 at a certain time-elapsed since recon-nection. The maximum energy of injected ions with detectable fluxes is eim. Thepoint C in the cusp ionosphere is a distance dc1 downstream from the ionosphericfootprint of P1 and a distance dc2 from that of P2 . Ions of energy eim from P2

reach the point C, where Eq. 24 shows eim = (m/2)(d Vc/dc2)2. Ions of energy eic =(m/2)(d Vc/dc1)2 reach C from P1. Because dc1 > dc2 , eic < eim and because P1 isthe edge of the source region, dc1 is a maximum and thus eic is a minimum. Hencea range of ion energies between the maximum, eim , and the lower cut-off, eic ,would be seen at C, corresponding to the range of source locations between P1

and P2. Putting in typical values, Lockwood and Smith [1993] show that thesource region for the cusp particles must be at least 10 RE in extent along themagnetopause.

Figure 9b also shows the trajectories of the ions and electrons from P1 having

the maximum energies with detectable fluxes, eim and eem . From Eq. 24, the

peak-energy electrons reach the ionosphere at a distance de downstream from the

OCB and form what is called the electron edge [EE] because no electrons can bedetected upstream of this. The ions have a corresponding edge [IE] at di from theOCB, where di » de because mi » me and ei ~ em [Eq. 24]. Gosling et al. [1990c]

have reported a satellite pass near the magnetopause which showed exactly thispredicted structure of electron and ion edges near the magnetopause. Theobservations also showed the corresponding evolution of the variousmagnetospheric particles as they began to escape along the opened field lines intothe magnetosheath. However, it can also be noticed that although injectedelectrons were detected between the electron and ion edges, they were of lowflux, and the electron flux increased considerably as the satellite crossed the ionedge, into the accelerated flow region where D-shaped injected ion distributionswere observed. This phenomenon is not predicted for a simple velocity filtereffect on the electrons, and is even more marked in the ionosphere [see Onsageret al., 1993]. The answer is almost certainly associated with the fact that the cuspappears to remain quasi-neutral, i.e. the density of injected electrons remainsalmost equal to that of the ions [Burch, 1985], thus between the ion and electronedges few electrons precipitate because there has not yet been time for the ions toreach the ionosphere.

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6.2. The magnetic cuspThe name "cusp" is derived from the dayside magnetic topology of field lines

which extend to the dayside magnetopause. The concept of the cusp is as old asthat of the magnetosphere itself, as both first appeared in the paper by Chapmanand Ferraro [1931] [who called the magnetic cusps "horns"]. In figure 1, themagnetic cusp is the point about which the Chapman-Ferraro currents circulate.In a fully-closed magnetosphere, like that initially considered by Chapman andFerraro, the cusp field line maps to a neutral point on the magnetopause.

In an open magnetosphere, a boundary-normal field Bn is added to those partsof the magnetopause where the newly-opened field lines evolve away from thereconnection site, which is very likely to include the magnetic cusp region.Typically field lines evolve along the magnetopause at Vf ~ 250 km s-1, whereasthe ionospheric convection speed is ~ 1 km s-1. From Eq. 14 this corresponds toan ionospheric electric field of ~ 50 mV m-1, given that the ionospheric field is Bi

= 5 × 10-5 T . The boundary tangential electric field at the magnetopause can thenbe estimated for steady-state cases using Eq. 23 to be Et ~ 1 mV m-1 [thisemploys a circular flux tube with a typical magnetosphere field just inside theboundary of Bsp = 20 nT so that dlm/dli = (Bi/Bsp)½ = 50 ]. Because Vf = Et/Bn wetherefore find that the boundary normal field is typically Bn ~ 4 nT. Thus theboundary normal field is small compared to Bm and does not fundamentally alterthe basic cusp topology.

There is, however, a significant effect of boundary-normal field on how fieldlines map from the magnetopause to the ionosphere. If we consider a fully-closedmodel of the magnetosphere, the entire magnetopause maps to a point cusp [as,for example, in the empirical Tsyganenko models in which the boundary-normalfield is zero almost everywhere because of the way the models are constructed].However, if low-latitude reconnection commences with constant voltage of 100kV, the area of the cusp in the ionosphere grows at 105/(5×10-5) = 2 × 109 m2s-1

and this growth continues for about 12 min., until the precipitation on the first-opened field lines is no longer called cusp [Lockwood and Davis, 1995]. By thistime, the area of the ionospheric cusp has grown from 0 to its maximum of 1.44 ×106 km2 . Given that the peak cusp width is observed to be roughly 5° of latitude[about 600 km], this means the longitudinal extent has grown to about 2000 km.This "opening" of the cusp has been modelled by [Crooker et al., 1991]. Figure 1is for equinox conditions whereas at the sol-stices the summer magnetic cusp istipped toward the sun, while the winter cusp is tipped away. These dipole tilteffects will also have a diurnal variation.

158

1 2

3

4

0 VFX

3 421

eic

eim

FXmv2 /2

dis

trib

utio

nfu

nct

ion

,f(

v)

ion velocity, v

time t

time t

y

x

observation time, ts

ion

en

erg

y,e i

OCB

cleft cusp mantle

tx ty

Figure 10. Injected magnetosheath ions at the magnetopause and in the ionosphere, and theirevolution with time elapsed since reconnection. (a) shows the field-parallel sections 1-4 of theCowley-D distribution functions in the (open) LLBL, injected across the magnetopause whenthe field line is at the X-line (1) and in positions 2-4 shown in figure 5. Because of time-of-flight effects, these are dispersed along the corresponding dashed lines in (b), which is anenergy-time spectrogram for the steady-state case, also showing the minimum (eic) andmaximum (eim) energies of detectable ion fluxes. The latter is set by the one-count level of theinstrument which typically varies with ion velocity as shown by the thicker solid line in (a).The distribution function seen at time tx (in the cusp) and at ty (in the cleft) are shown in part(a) by dotted and dashed lines, respectively. The solid squares and open circles show thecorrespondence of points in (a) to those in (b). [After Lockwood, 1995]

6.3. The particle cuspThe discovery of magnetosheath-like plasma precipitating inside the

magnetosphere [Heikkila and Winningham, 1971; Frank, 1971] was initiallyinterpreted in terms of particle entry at the null points of the magnetic cusp; hencethe particles were given the name "cusp". However, transfer of plasma into a nullpoint is not an adequate explanation because a breakdown of frozen-in is stillrequired to give transfer onto magnetospheric field lines. In addition, as shown insection 6.1, the dispersed cusp ion precipitation, with a range of energies seen atany one point in the ionosphere, rules out any point-like source like a magneticnull [Lockwood and Smith, 1993; Onsager et al., 1993]. It was soon realised thatmagnetosheath plasma precipitated over a broad local time sector on the dayside,and so the additional concept of the "cleft", mapping to a closed LLBL field linetorus containing sheath plasma, was introduced by Heikkila [1972]. Mechanismsfor populating a closed LLBL with sheath plasma have been controversial, onepossibility being the re-closure of open flux during northward IMF which is

159

v v

v v

Z

XY MP

contours of N

flow streamlines

X-line

contours of time elapsedsince reconnection

v v

(a). (b).

(c).

Figure 11. Flows and magnetosheath plasma densities for the situation described in figure 5.(a) is the view of the dayside magnetopause from the sun with the concentric circles beingcontours of the magnetosheath plasma density (just outside the magnetopause) and the ar-rows showing the magnetospheric flow streamlines (just inside magnetopause) along whichthe newly-opened field lines evolve (see figure 5a). Viscously-driven flows are shown on theflanks of the magnetosphere. (b) and (c) show the corresponding steady-state ionosphericflows in both hemispheres (figure 5b) along with contours of time-elapsed since reconnectionin (b) and precipitating magnetosheath plasma density in (c).

illustrated in figure 8 [Song and Russell, 1992] which has been simulated usinga global MHD model by Richard et al. [1994]. Alternatively smaller-scalepatchy reconnection may do the same job [Nishida, 1989]. However, there is anargument that says there is no need to invoke a closed LLBL to explain cleftprecipitation, as will be discussed below.

Hill and Reiff [1977] showed that the cusp ions precipitation did include ionenergies consistent with the accelerated ions seen at the dayside magnetopauseand recently Lockwood et al. [1994] have deconvolved the time-of-flight effectsto show the precipitating ions to be consistent with the truncated, drifting Max-wellian at the dayside magnetopause, as predicted by Cowley [1982]. Thus thecusp is the ionospheric signature of the accelerated flows seen on the daysidemagnetopause.

If we consider a field line in position 5 in figure 6 [for southward IMF], asatellite observing it in the ionosphere will see no ions from the point where itpresently threads the magnetopause because they have not had time to reach theionosphere. It will, however, be able to see ions from where the field line used tothread the magnetopause, when it was in positions 2-4. The highest energy ionswould come from when the field line was in position 4 , whereas the lower cut-off

160

energy ions would have the longest time of flight and would have come from theX-line [hereafter called position 1], as illustrated in section (6.1). From the theoryof the ion injection and acceleration discussed in section (4.5), along with theCowley and Owen [1989] model of how a field line accelerates under magnetictension and the sheath flow [i.e. how Vf varies with position], we can derive thesequence of injected ion spectra shown in figure 10a for the field line positionsshown in figure 6 [Lockwood, 1995a; b; Lockwood and Smith, 1994]. Notice howthe minimum ion velocity Vmin rises between positions 1 and 2 as Vf increases,

but subsequently falls to zero as θ increases to greater than π/2. These truncated,drifting Maxwellian spectra are the field-parallel part of the Cowley-Ddistributions which reach the ionosphere without mirroring [see figure 3c]. Theion spectra injected at any one point on the magnetopause are then dispersed inposition according to Eq. 24, such that a satellite intersects different energies atdifferent times. The dashed lines in figure 10b show where the spectra in 10a aredispersed . The plot is in the energy-time spectrogram format, showing the ionenergy ei as a function of observing time, ts. This case is for a satellite which ismoving poleward when the IMF Bz < 0 so that it is moving away from the open-closed boundary. The dashed lines are given by Eq. 24 with a satellite velocity Vs

= dc/ts. Figure 10b also shows the minimum [eic] and maximum [eim] detected ionenergies as solid lines. The minimum is set by the time-of-flight cut-off but themaximum is where the distribution function falls below the minimum detectablevalue, the "one-count level" shows as a solid line in 10a.

At time ts = 0 the satellite crosses the OCB. At tx, it sees ions which wereinjected when the field line was in a range of positions, including 1 and 3, and thespectrum is as shown by the dashed line in figure 10a: the open circles in both 10a

and 10b show the part injected when the field line was in positions 2 and 3[remember both ei and f(ei) are conserved for adiabatic scatter-free motion]. At alater ts [= ty ], when the satellite is further poleward, it sees the spectrum given bythe dotted line [the solid squares showing those ions injected when the field linewas in positions 1, 2 and 3]. In both cases, a clear cut-off energy [eic in 10b] isseen. All ions at the cut-off come from near the reconnection site [Lockwood etal., 1994]. The spectrum seen at ty is very like that in the magnetosheath andwould be classified as "cusp", whereas that at tx has higher average energy andlower density, and would almost certainly be classified as "cleft". Figure 10b

shows that, in this case, they do not differ in the injection and transport processesand if one thinks of cleft as the projection of the LLBL it is here on open, notclosed, field lines. As the time elapsed since reconnection increases theprecipitation evolves from cleft to cusp to other classifications called "mantle"and "polar cap" [Cowley et al., 1991a]. This is a key feature of the plasma entry

161

facilitated by reconnection. All the characteristics of the precipitating ions[including the cut-off energy, eic, the density, N, and the temperature, T] evolveas a function of time elapsed since reconnection as the field line migrates fromthe reconnection site into the tail lobe. From the above discussion, we see thatthis evolution has three causes: the changing characteristics of the sheath at thepoint where the field line threads the boundary; the changing ion acceleration oninjection across the boundary; and the time-of-flight dispersion effects.

However, figures 6 and 10 are two dimensional and apply to the noon-midnightmeridian only. This is investigated in figure 11. Figure 11a is a view from thesun, with an X-line lying in the equatorial plane. The streamlines, along which thenewly-opened field lines evolve away from the X line over the magnetopause, areshown along with the circular contours of magnetosheath density at the boundary.Parts (b) and (c) show the corresponding ionospheric flow streamlines, as infigure 6b. Figure 11b also shows the contours of time-elapsed since reconnectionand 11c shows the precipitation density, N. Along each streamline, the numberdensity firstly rises with elapsed time since reconnection [as lower-energy ionshave time to arrive] but then it maximises and falls because the particles begin toflow superthermally away from the Earth instead of precipitating. This can beseen in figure 11c. However, there is another factor highlighted by 11a, namely

that the field lines reconnected near the X axis [Y ≈ 0] will experience higherdensity inflow than those reconnected at larger |Y|, where sheath densities arelower. This is manifest as a local time variation in densities, which peak nearnoon in 11c. In addition, the field line velocity Vf will be larger away from thestagnation region and so the ion acceleration will be greater [giving larger ionenergy, e] at greater |Y| where N is lower.

It is thus possible that the lower N/higher e precipitation away from noon is nota closed LLBL [cleft] precipitation, but also arises from the same processes as thehigher density and lower energy cusp precipitation, as must be the case for thecleft near noon. This is consistent with the statistical patterns of the variousclassifications of magnetosheath precipitations presented by Newell and Meng[1992]. If we separate the precipitation into classifications of cleft, cusp, andmantle using the densities, figure 11c looks very much like the Newell and Mengpatterns. These statistical patterns show cleft and mantle precipitations coveringthe same broad MLT extent of the dayside, which is consistent with the idea thatthey share the same injection and transport processes: given that the mantle is onopen field lines this implies the cleft is also. Figure 11c shows why the higher-density cusp has a somewhat smaller MLT extent. The origin of the small step inthe characteristics used by Newell and Meng [1988] to distinguish cleft from cuspis unclear in this interpretation.

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6.4. The cusp auroraThe magnetosheath electrons and ions which precipitate into the cusp/cleft

ionosphere generate a characteristic aurora. The relatively low energies of theseparticles means that the aurora is dominated by 630 and 636.4 nm [red line]emissions of atomic oxygen, with much lower intensities of the 557.7 nm [greenline]. This is because the 1D2 electron state is readily excited [1.96 eV aboveground state, the 3P doublet] whereas very few atoms are excited to the 1S0 [4.17eV above the 3P]. The excitation is largely caused by the elevation of theionospheric electron temperature such that the electrons on the hot tail of theionospheric gas are very efficient in exciting the 1D2 state [Rees and Roble, 1986;Mantas and Walker, 1976; Wickwar and Kofman, 1984].

A complication in interpreting images of the cusp/cleft emissions is that the1D2 state de-excites [with the emission of a red line photon] after a radiativelifetime which, if unquenched, has a value of 110 s [compared with 0.74 s for thegreen line]. During this time the excited atomic oxygen moves with thethermospheric wind [typically 0.5 km s-1] and so emission occurs at an averagedistance of ~110 × 0.5 = 55 km downwind from the point of excitation. However,there is a spread of lifetimes, and hence distances, if quenching by collisions ispresent, and the image will be smeared. In addition, the altitude of the excitationis not well known and a lower altitude gives more quenching and the lifetime isreduced.

A region of dominant red-line emission was first reported by Sandford [1964].This was shown to poleward of the more energetic dayside auroral precipitationby Eather and Mende [1971]. The association with the newly-discovered cuspprecipitation was made by Heikkila [1972]. Recent observations have shown thatthis red-line aurora either contains, or is made up of, a series of poleward-movingevents when the IMF is southward [e.g. Sandholt et al., 1985; 1992; Fasel, 1995].

6.5. The cusp ionosphereThe electron heating in the cusp region which was invoked above as a major

cause of the cusp/cleft aurora was inferred in a statistical survey of the topsideionosphere by Titheridge [1976] and has been directly observed by satellite[Brace et al., 1982; Curtis et al., 1982] and incoherent scatter radar observations[Wickwar and Kofman, 1984; Watermann et al., 1994]. With very high timeresolution [10s] measurements, Lockwood et al. [1993] have recently reportedthat the electron temperature enhancements can sometimes only consist of a seriesof poleward-moving events, very similar to the behaviour of the red-line auroraltransients mentioned in the previous section.

163

v v

v v

Z

XY MP

contours of Nv

flow streamlines

X-line

v

(a). (b). Northern hemisphere

(c). Southern hemisphere

Figure 12. (a) is equivalent to figure 11, for the case with IMF Bz > 0, IMF By > 0 and re-connection in the northern hemisphere lobe only. (b) and (c) are equivalent to figure 11(c),for the northern and southern hemisphere ionospheres, respectively.

The behaviour of the plasma densities in the cusp/cleft region is complex. Theprecipitating particles enhance the densities as well as the electron temperatures.However, unlike the temperature which reaches peak values almost instantly afterthe precipitation commences, the density grows while the precipitation per-sists[Whitteker, 1977; Watermann, 1994]. Note that this residence time of a fieldline in the cusp precipitation region does not depend on the ionospheric convec-tion speed, but on how quickly the field line evolves over the magnetopause tothe region where the flow is superthermally tailward thereby cutting off access tothe ionosphere. We can estimate the residence time from the behaviour of thelow-energy cut-off ions observed in the cusp: eic in the cusp region falls fromabout 5 keV to 100 eV which, for a distance of 16 RE from the X-line to theionosphere, correspond to flight times of about 104 s and 737 s, respectively.During the difference in time-elapsed since reconnection of 10.5 min., the cusp isseen. This is sufficient for a considerable enhancement of the F-region [a factorof about 2-4 over typical winter values]. However, the cusp region is also wherethe tension force on newly-opened field lines can generate fast convection in theeast-west direction if |By| is large [section 5.4]. These fast flows act to deplete theplasma and reduce the enhancement caused by the cusp precipitation [Rodger,1994]. The fast flows will also cause strong ion heating, a molecular rich iono-

164

sphere, anisotropic and non-Maxwellian ion velocity distributions and are verylikely to be involved in generating the plasma upflows into the magnetospherethat are called the cleft ion fountain [Lockwood et al., 1985a; 1985b].

6.6. The cusp currentsSections 6.1-6.5 show that the term cusp is applied to many different

phenomena. Another example of this are the By-dependent field-aligned currentswhich bring the east-west flows associated with the Svalgaard-Mansurov effect tothe ionosphere [McDairmid et al., 1978; Taguchi et al., 1993]. These are oftenreferred to as the cusp currents. Some authors have preferred the title ’mantle’currents because they are sometimes found in the precipitation region termedmantle, rather than in the cusp precipitation region. This debate is bestunderstood in terms of the evolution of the newly-opened field lines: theprecipitation evolves from cusp to mantle classifications roughly 12 min afterreconnection [see the previous section]. This is also roughly the time scale for afield line to straighten. As the field-aligned currents on newly-opened field linesare associated with this unbending, we should expect them to be close to thecusp/mantle boundary, but they can be in either region in any one case. Thepattern of field-aligned currents for non-zero IMF By shown in figure 4d wasproposed by Cowley et al. [1991b] from considerations about how newly-openedfield lines will evolve. Thus they were able to make predictions of where theparticle precipitations of various classifications will be seen relative to the field-aligned currents. Initial studies by de la Beaujardiere et al. [1993] are consistentwith these predictions.

6.7. The northward IMF cuspI have concentrated on the cusp during southward IMF. This is because

relatively little is known, and even less understood, about the northward IMFcusp. Figure 12a corresponds to figure 11a for the case with a lobe reconnectionsite in the northern hemisphere and IMF By > 0. Figure 12b shows the circulationin the open field line region which results, as discussed in section (5.5). Thereconnection reconfigures open field lines which thread the magnetopause fardown the tail and along which there is little or no cusp precipitation. Afterreconfiguration the field line thread the dayside magnetopause and cuspprecipitation results with reverse dispersion seen where the convection issunward [figure 12b].Woch and Lundin [1992] have demonstrated that theaccelerated ions are found on the poleward edge of such reverse dispersionsignatures for sunward convection during northward IMF, as opposed to theequatorward edge for antisunward convection during southward IMF. In the otherhemisphere [figure 12c], there is no lobe circulation and field lines only thread thetail magnetopause. Thus there will be little magnetosheath-like precipitation, andany there is will continue to decay in energy and density as the field lines are

165

further extended down the tail. Following a turning of the IMF from southward tonorthward, the precipitation may persist for longer than the time constant withwhich the flow in the polar cap decays and then we may be able to observe astagnant cusp precipitation, albeit briefly [e.g. Potemra et al., 1992]. However,the time constant for flow decay appears to be 10-20 min. [see sections 5.2 and7.2] which is comparable with, or longer than, the time of about 12 min. in whichthe precipitation classed as cusp evolves into the precipitation classed as mantle.Thus observations of a broad, stagnant cusp precipitation during northward IMFcould imply that the satellite is moving roughly perpendicular to the flowstreamlines and along lines of constant elapsed time since reconnection [e.g. ameridional pass at noon in figure 12b].

Another possibility is that field lines have been reconnected away from thenose of the magnetosphere, such that the tension force is closely matched to andalmost balances the sheath flow. In such cases, it may be possible for the fieldline to be held for an extended period such that it threads the daysidemagnetopause, thereby generating a stagnant, undispersed yet dense cuspprecipitation. Note that the small Vf would mean that there would not be anyaccelerated ions in such cases.

7. Non-steady stateIn section 6, brief mention was made of recent observations of transient events

in the dayside cusp region. It is not a coincidence that these have all beendetected using ground-based instruments. Satellite data suffer from what isknown as spatial/temporal ambiguity. For example, a low-altitude satellite has anorbital period of about 90 min. By comparing data from successive orbits we canstudy fluctuations which are of period 90 min. or greater. Similarly, if we are notconcerned with spatial structure of scale less than, say, 10 km [which the satellitecovers in about 1 s], we can study fluctuations of 1 s or faster using the satellite.However, there can be no information on the range of periods between about 1sand 90 min from such an ionospheric satellite. Ground-based remote-sensinginstruments, on the other hand, can observe the same region of space for severalhours and can achieve time resolutions of 1s or less. Thus they are ideal forobserving the periods which satellites cannot.

One of the key variations which has been studied in the ionosphere is thesubstorm cycle [period usually 1 - 3 hours]. On the dayside, there has also beenmuch interest in fluctuations in the cusp region on time scales of several minutes.Both are beyond the Nyqvist sampling limit of ionospheric satellites.

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7.1. Substorm growth phaseCareful inspection of figure 1 shows that some of the Poynting flux flow lines

[dashed lines] which emanate from the HLBL end in the tail lobe rather than atthe tail neutral sheet. The lobe is a sink of Poynting flux if there is a positive∂€W/∂€t [Eq. 21] and energy is stored as magnetic energy because the tail lobe fluxincreases. This storage can be because either the lobe field increases or the tailcross section area increases [tail flaring], or both. In either case, the total tail lobeflux increase is caused by the rate at which field lines are opened at X exceedingthe rate at which they are closed at Xt. Such an imbalance is expected following asouthward turning of the IMF, when the dayside reconnection responds veryrapidly to the appearance of increased magnetic shear across the low-latitudemagnetopause. However, there is no way that this information can be transmittedto a distant X-line in the tail, where the reconnection remains unaffected for aperiod of 30 min. or more [Cowley and Lockwood, 1992]. By Faraday’s law, thedifference between the dayside and nightside reconnection voltages is the rate ofincrease of the open flux [∂€F/∂€t > 0]. This corresponds to an increase in theenergy stored and, because the ionosphere is incompressible, will be signalled byan increase in the area of the open field line region in the ionosphere [Akasofu etal., 1992]. From Eq. 23, this rate of change of the lobe flux causes the steady-state electric field mapping to break down, such that the dawn-dusk electric fieldin the ionosphere is less than it would be in steady state. Thus the electric field inthe HLBL during the growth phase has two effects: it causes deposition of energyin the tail and causes some flow/electric field in the ionosphere. The latter iscalled the directly-driven system. When averaged over several substorm cycles,there is no nett change in F and so there must be other periods in the substormcycle [in the expansion/recovery phases] in which there is destruction of lobeflux. The flows/currents associated with release of the stored energy/flux in thetail lobe is called the storage system. Thus on average, steady-state mapping ofelectric fields from the magnetopause to the ionosphere will apply, but it does notapply at any one instant. This was deduced from observations of the response ofionospheric convection to changes in the IMF by Lockwood et al. [1990]. Theseobservations indicate the 10-20 min inductive smoothing time constant [for bothrising and falling flows] discussed insection 5.2.

These concepts have been vital in understanding non-steady state situationsfollowing changes in IMF orientation [Lockwood et al., 1990]. The variability ofthe polarity and strength of IMF Bz [Lockwood, 1991; Lockwood and Wild, 1993]is such that it fluctuates much more rapidly than the time constant for themagnetosphere-ionosphere system to approach steady state, and we shouldtherefore expect non-steady behaviour to be normal rather than exceptional andthe ionosphere-magnetosphere system to usually be in non-equilibrium states oftransition. Indeed, it is possible that the rare steady convection events [also called

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convection bays, Sergeev et al., 1994] are caused by a coincidental IMFfluctuation which happens to cause the dayside reconnection voltage rate toremain close to that in the nightside tail for an extended period.

S

1

2

34

m(a). (b).

Figure 13. Ionospheric flow for the non-steady state magnetosphere-ionosphere system whenthe dayside reconnection voltage exceeds the tail reconnection voltage, as during substormgrowth phases. This causes expansion of the polar cap region of open flux, as shown by thesolid arrows. The merging gap is shown as a dashed line and adiaroic segments of the open-closed boundary are solid lines. Note flow streamlines cross the moving adiaroic boundaries(in the Earth’s frame) although the plasma and frozen-in flux do not: no reconnection istaking place at the corresponding segment of the magnetopause and the boundary and plas-ma move together in the boundary-normal direction. (a) flow for IMF Bz < 0, By = 0 . (b).flow in the northern hemisphere for pulsed reconnection for IMF Bz < 0, By > 0. The regionsof newly-opened flux 1-4 are produced by successive reconnection bursts. S shows a typicalpath of a low-altitude polar-orbiting satellite and m the meridian scanned by a dayside auro-ral photometer.

7.2. The behaviour of the open-closed boundarySiscoe and Huang [1985] introduced the important concept of non-

reconnecting parts of the magnetopause which map to "adiaroic" [meaning "notflowing across"] segments of the open-closed boundary in the ionosphere. In theboundary rest frame, the flow speed must be zero [there is no flux transport fromclosed to open field lines, i.e. no reconnection]. However, if the adiaroicboundary moves in the Earth’s frame, this means that there will be plasma/fieldline flow in the Earth’s frame also. As a result, flow streamlines will cross movingadiaroic segments of the open-closed boundary, although the plasma and frozen-in flux tubes do not cross the boundary. This cannot happen in steady state, forwhich there are no boundary motions and hence flow streamlines only cross theopen closed boundary at the merging gaps.

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The fact that electric fields do not map from the magnetopause to theionosphere is also important to our understanding of how the open-closedboundary will behave. Until recently most data was of poor time resolution or sohighly averaged that scientists became very familiar with the steady-stateconcepts of mapping electric fields. However, consideration of one of a numberof non-steady situations soon leads to an appreciation that this concept cannot beapplied on shorter time scales. For example, following a northward turning of theIMF, the noon open-closed boundary [and the last-to-have-been-opened fieldlines immediately poleward of it] initially relax poleward. However, thesubsequent behaviour if the IMF persists in its northward orientation reveals thatmagnetopause electric fields do not map to the ionosphere. Were themagnetopause electric field to map to the ionosphere in this case, the last-openedfield lines [still in the solar wind and thus still subject to the dawn-to-duskmotional electric field] and the open-closed boundary would continue to migratepoleward and into the nightside. This does not happen. The cusp/cleft auroraceases moving poleward roughly 10-20 min after a northward turning andsatellite particle observations do not reveal such nightside locations of thesunward edge of the polar cap boundary. Because there is no low-latitudereconnection, the dayside polar cap boundary will be adiaroic following anorthward turning. Thus there will initially be poleward flow at the same speed asthe boundary motion, but both this flow and the boundary motion will decay overthe 10-20 min inductive smoothing time.

Siscoe and Huang [1985] demonstrated how a two-cell flow pattern can arisefor a simple circular and expanding polar cap, with dayside but no nightsidereconnection [i.e. in the growth phase of a substorm]. This situation is depicted infigure 13a. The dashed line maps to an active dayside reconnection X-line. Theflow into the polar cap causes it to expand. The solid segments of the open closedboundary are adiaroic and these expand outward, as shown by the thick arrowsnear dawn and dusk. The plasma and frozen-in flux tubes move with the adiaroicboundaries and the flow streamlines cross the boundary, although there is noclosure of the open flux there.

7.3. Effects of reconnection rate pulsesSection 4.6 discussed how reconnection rate pulses are thought to generate

characteristic signatures at the magnetopause called flux transfer events. In recentyears there has been much interest in understanding what the ionosphericsignatures of such events would look like and hence determining their size andcontribution to the total flux transfer rate from the dayside to the nightside [i.e. tothe transpolar voltage Φpc].

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Given that the ionospheric flows have a 10-20 min. rise time following areconnection pulse, a short pulse will initially cause the open-closed boundary tomigrate equatorward, rather than exciting poleward flow. This effect is seen inthe equatorward edge of cusp precipitation [Burch, 1973], in radar observationsof the cusp [Foster et al., 1980] and in optical observations of the cusp/cleftaurora [Sandholt et al., 1985; Pudovkin et al., 1992]. Cowley and Lockwood[1992] have provided an explanation of the subsequent flows as themagnetosphere-ionosphere system attempts to return equilibrium with the newamount of open flux, with reduced magnetic flux in the dayside magnetosphereand more in the tail lobe. A key prediction of this model is that each region ofnewly-opened flux produced by a reconnection burst is appended directlysunward of that produced by a prior reconnection burst and these regions areabutted up against each other. This situation is shown in figure 13b. In this sketch,the reconnecting segment of the open-closed boundary [dashed line] has justproduced the patch 4 by migrating equatorward in response to a fourthreconnection pulse. The previous three pulses produced patches 1-3, which areabutted and separated by dotted lines. The flows and evolution of the patches areshown for IMF By weakly positive in the northern hemisphere. If thereconnection pulses repeat on a period shorter than the inductive smoothing time,the poleward flow will be relatively constant and the patches produced bysuccessive reconnection pulse drift poleward together. This gives an explanationof the poleward-moving events of enhanced electron temperature [Lockwood etal., 1993] and of the red-line auroral transients in the cusp region [Sandholt et al.,1992].

A reconnection pulse must give growth in area of a patch of newly-opened fluxin the ionosphere and we would expect magnetosheath electron precipitation onthese newly-opened field lines. The patch of 630 nm-dominant aurora thusformed should then migrate with the newly-opened field lines and fade as thethey become appended to the tail lobe [10-20 min later]. The direction of themotion would initially be controlled by the polarity of the IMF By component, bythe Svalgaard-Mansurov effect. Later in their lifetime, when the magneticcurvature force is reduced, events would move more poleward under theinfluence of sheath flow. All these features are indeed observed in transient cuspevents seen in 630 nm emissions [Sandholt et al., 1992; Lockwood et al., 1995].Furthermore, simultaneous radar data show that there are plasma flow burstswithin each optical event when |By| is large, and the plasma moves with the samevelocity as the event as a whole, as expected if the patch is made up of newly-opened field lines produced by a reconnection burst [Lockwood et al., 1989].Pinnock et al. [1993] have shown that one of a string of such flow bursts was anelongated channel coincident with the cusp precipitation. The occurrence of theseevents is very similar to that of FTEs, in that they occur almost exclusively duringsouthward IMF when they repeat with a skewed distribution of periods about a

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mean of 7 min [Fasel, 1995], strikingly similar to that for FTEs [Lockwood andWild, 1993]. The evidence that they are caused by reconnection pulses and thusrelated to magnetopause FTEs is therefore very strong indeed. However, on onlyone occasion have simultaneous observations of the two phenomena beenpossible [Elphic et al., 1990].

Figure 13b also provides an explanation of the phenomenon of cusp ion steps.Because each patch is produced by a discrete reconnection burst, the elapsed timesince reconnection changes discontinuously across the boundaries which separatethe events. Section (6.3) showed how the cusp precipitation characteristics are afunction of the time elapsed since reconnection [including the lower cut-offenergy, eic , and the density, N]: thus we expect discontinuous changes in theprecipitation at each step, as seen for example by the satellite S at p in figure 13b.Cusp ion steps were predicted from the flow excitation theory of Cowley andLockwood [1992] by Cowley et al., [1991] and were independently reported inobservations by Newell and Meng [1991]. Lockwood and Smith [1992] haveinverted the theory to allow the reconnection rate to be computed from thedispersion characteristics. Lockwood and Smith [1994] have extended the theoryto allow for cases when the satellite is moving toward/away from the open-closedboundary more slowly than the convection speed [i.e. longitudinal passes by anionospheric satellite or for a mid-altitude satellite]. In these cases the steps cantake on a variety of different forms. The observations by Lockwood et al [1993]of cusp ion steps on the boundaries between poleward-moving events areimportant support for the theory of the effects of pulsed reconnection as theyshow that the two predicted features are indeed related.

7.4. Travelling convection vorticesThere are other transient events in the cusp ionosphere which have not

received much attention in this tutorial. Chief amongst these are travellingconvection vortices [TCVs] which are seen throughout the dayside, usually usingchains and networks of magnetometer stations [Friis-Christensen et al., 1988;Glaßmeier et al., 1989]. These events appear to travel away from noon around thepolar cap boundary in both the afternoon and morning sector, unlike the By-dependent motion of the poleward-moving auroral and radar events discussed inthe previous section. They have the form of a matched pair of filamentary fieldaligned currents, like figure 5, but whereas an FTE event would move in thedirection from C to D, such that the convection velocity in the event centre wasequal to the phase velocity of the event, TCVs travel perpendicular to thatdirection and at a faster phase speed [of order 5 km s-1]. There are flow vorticesassociated with these events [speeds of about 1 km s-1] [Lühr et al., 1995] and asan event passes east/west over a meridian, a tripolar poleward flow signature isseen for a twin vortex event. This is very different from the reconnection pulseevents [for which the inductive smoothing yields a steady poleward flow with a

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small modulating ripple at the frequency of the reconnection pulses, along withperiodic longitudinal flow bursts if the IMF |By| is large]. TCVs have in the pastbeen confused with FTE flow burst events, for example, it is now clear that theflow burst event described by Todd et al. [1986] was in fact a TCV [Lühr et al.,1993]. Similarly, what are now called TCVs have also been interpreted as rapidmotions of the cusp [Potemra et al., 1992] and so-called plasma transfer events[Heikkila et al., 1989].

TCV's have been linked with buffeting of the magnetosphere by solar winddynamic pressure changes, and this is an integral part of the theory of Kivelsonand Southwood [1991]. The resulting propagating deformation of themagnetopause causes a flow vorticity and drives the filamentary field-alignedcurrents. The phase motion of the events then corresponds to the motion of thedeformation around the magnetopause. However, one major mystery is theappearance of magnetosheath-like precipitation in these events, particularly in theupward field-aligned current filament [Potemra et al., 1992], causing an auroraltransient which appears to be on closed field lines as it moves longitudinallyequatorward of the cusp/cleft aurora [Lühr et al., 1995; Heikkila et al., 1989].TCVs do often occur in a series of events, and this may offer an explanation of themultiple injection events, seemingly onto closed field lines, reported by Wochand Lundin [1991]. One valid and viable mechanism, which may fit with thedynamic pressure pulse model of TCVs, is of enhanced magnetosheath densitypatches which indent the magnetopause to the extent that reconnection takesplace behind the embedding filament, as simulated by Ma et al. [1991]. However,these ideas remain mere speculation in relation to TCVs at the present time.Lockwood [1995b] has shown that some of the multiple injection events may befitted into a single X-line reconnection model if fluctuations in the sheath densitycause changes the magnetopause Alfvén speed.

7.5. Poleward-propagating longitudinal flow changesSection 5.4 showed how longitudinal flows in the dayside cusp/cleft

ionosphere were driven when the IMF Bz < 0 and |By| is large, by the magneticcurvature force on the newly-opened field lines. Thus if the IMF By showsperiodic oscillations during southward IMF, we would expect the longitudinalflow in the ionosphere to oscillate in polarity [provided the period is not too shortcompared to the response time]. These changes would migrate poleward with thereconnection-driven antisunward flux transfer. Such events have recently beenreported by Stauning et al. [1994] and fit very well with the expectations of themagnetic curvature force effect. Several authors have suggested that thesepoleward-moving disturbances are the same as the poleward-moving transientevents discussed in section 7.3 and thus the latter are simply the effects of IMF By

changes with steady reconnection rate [e.g. Newell and Sibeck, 1993]. However,

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this would produce a patch of red-line aurora of roughly constant area whichwould be swept back and forth in the east-west direction by the flow changes: infact the poleward-moving auroral events show consistent and repetitive motion tothe east or west [depending on the sense of the IMF By] [Lockwood et al., 1995].In addition, the flow bursts are still seen when the IMF By is large but steady.Hence these two phenomena are quite distinct.

8. SummaryThis tutorial has given the basic concepts which allow us to gain a consider-

able understanding of how energy, mass and momentum are transferred fromthe solar wind into the ionosphere. The basic of paradigm of ideal MHD ap-plying everywhere, except at a few localised breakdowns where reconnectiontakes place, as originally conceived by Dungey [1961], is remarkably success-ful. One might have expected progress in recent years to have revealed morecases in which this paradigm is inadequate. However, the opposite has provento be true and our improved understanding has allowed more phenomena to beunderstood in these terms. In addition, the publication record shows that thismodel is the only one which has had genuinely predictive power in the area ofsolar-wind magnetosphere coupling. Numerical simulation results increasinglyare able to reproduce simpler conceptual explanations. However, this is not tosay that all is understood. Some key areas where our understanding is lackinginclude: the maintenance of cusp quasi-neutrality; the origin of structured cuspelectron precipitation [and hence of the gaps between the 630 nm transients];the electron acceleration to give 557.7 nm transients; the origin of magne-tosheath-like precipitation in TCVs; origins of multiple injection events; effectsof magnetosheath Alfvén speed changes; the causes of viscous-like interac-tions; the variations of the inductive smoothing time constant and its effects;the spectrum and causes of reconnection rate variations in both time and space.With new facilities like the Cluster, Interball and Geotail satellite missions, theEISCAT Svalbard Radar, the CUTLASS SuperDARN radars and many others,we have a genuine opportunity to answer some of these puzzles.

Acknowledgements:

The author gives particular thanks to Prof. S.W.H. Cowley for his remarkably clear help,tuition and insight.

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10. Glossary of acronymsAU astronomical unit ( = distance from the

sun to Earth)CRB convection reversal boundarydHT de Hoffman-Teller (velocity/frame)FTE flux transfer eventGSM geocentric solar magnetospheric

(coordinates)HLBL high-latitude boundary layerIMF interplanetary magnetic fieldLHS left hand side

LLBL low-latitude boundary layerMHD magnetohydrodynamicsOCB open-closed (field line) boundaryPDL plasma depletion layerRD rotational discontinuityRE Earth radiusRHS right hand sideSTP solar terrestrial physicsTCV travelling convection vortexTD tangential discontinuity

11. Symbolsa angle of reconnection outflow wedgesds element of areadl element of lengthdlm length in the magnetopausedli length in the ionosphered field-aligned distance from X-line to

ionospheredc distance along flow streamlinee the charge on the electronei ion energyf distribution functiong acceleration due to gravityk Boltzmann’s constantm massq electronic charget timev velocityx axis normal to the magnetopausez axis in the magnetopause plane in

direction of VfA areaB magnetic field (or induction or flux

density)Bsh magnetosheath field near the

magnetopauseBsp magnetospheric field near the

magnetopauseBz northward component of B (usually of

the IMF)Bn outward normal field component to the

magnetopauseBi magnetic field in the ionospheric F-

regionE electric fieldEt tangential electric field component at

the magnetopauseEi ionospheric electric fieldF magnetic fluxFjk force on gas j due to collisions with gas

k

J current densityJCF magnetopause (Chapman-Ferraro)

current densityJP ionospheric Pedersen current densityLc characteristic plasma scale lengthN number densityP plasma pressureRm magnetic Reynold’s numberS Poynting fluxSv vertical component of ST plasma temperatureU relative velocity of two reference framesV plasma velocityVA Alfvén speedVc characteristic plasma scale speedVf field line velocity ( dHT frame velocity)Vmin minimum velocity of injected ion

populationVp velocity of peak of distribution function

(i.e. f(Vp) is a maximum)WB energy density in magnetic fieldWth energy density in thermal particle

motionsWV energy density in bulk flow of particlesX GSM axisY GSM axisZ GSM axisυjk the collision frequency for momentum

transfer between gas j and gas kσ electrical conductivityρ plasma mass densityµo the permeability of free spaceti ion time of flightΦ voltageΦpc transpolar voltageθ angle that magnetospheric field makes

with magnetopauseφ angle that magnetosheath field makes

with magnetopause

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AURORA/SUBSTORM STUDIES WITH INCOHERENT-SCATTER RADARS

Y. Kamide

1. IntroductionThe ultimate energy source of substorms and plasma convection in the magne-

tosphere is the solar wind. The ionosphere, particularly the polar ionosphere,where dynamic auroras occur and intense currents flow, couples electrically withthe magnetosphere through magnetic field lines. It can be said that the solar windtells the magnetosphere what to do [see Lockwood, 1996], although it does notgive detailed instructions as to how to do it. In other words, the solar wind pro-vides the magnetosphere with the boundary and initial conditions, and, giventhese conditions, magnetospheric and ionospheric processes such as substormsand plasma convection take place internally in the system.

The earth’s magnetic field connects the ionosphere at high latitudes and themagnetosphere, causing an exchange of energy and momentum between the tworegions. Thus, the ionosphere and the magnetosphere are coupled in so manydifferent ways that the subject of the magnetosphere-ionosphere system is notori-ously difficult to subdivide practically: all magnetospheric processes are con-trolled by electrodynamics in the ionosphere in some way, and all ionosphericprocesses bear on the multi-faceted state of the magnetosphere. Moreover, themagnetosphere-ionosphere system is intrinsically nonlinear and unsteady, and isaffected directly and indirectly by changes in the solar wind. The boundariesbetween any adjacent plasma regions of earth’s electromagnetic environment arenot simple, stationary, topological borders, but represent the dynamic areas whereunique physical processes operate. The coupling in the magnetosphere and thepolar ionosphere implies active interactions between hot but low-density plasmasin the magnetosphere and cold but high-density plasmas in the ionosphere[Baumjohann and Treumann, 1996].

Under this interaction mechanism, many exciting large-scale and small-scalephenomena, such as acceleration of charged particles, auroral displays, burst inelectric fields and currents, are occurring. Electric fields in the high-latitude iono-sphere and the associated magnetospheric plasma convection, which is induced bythe solar wind, change the morphology and composition of the ionosphere [seeSchlegel, 1996]. These changes in the ionosphere thus produce variations in thethermospheric structure and the neutral wind system [see Richmond, 1996]. It isthese variations in the ionosphere-thermosphere system that, in turn, modifymagnetospheric processes. The entire dynamic coupling chain takes place through

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fields, currents, heat flow and frictional interactions with their own characteristictime scales.

The purpose of this paper is to examine the degree to which spatial and tempo-ral variations in large-scale electromagnetic phenomena, such as auroras andelectric fields and currents during magnetospheric substorms, play a principal rolein the physical linkage involved in solar wind-magnetosphere-ionosphere interac-tions. It is demonstrated that the construction of incoherent-scatter radars andtheir subsequent upgrading in operational techniques during the last two decadeshave made it possible to unveil some of the basic characteristics of ionosphericparameters at the different phases of substorms. Radar data offer a unique oppor-tunity to understanding quantitatively the convection/substorm relationship ifexamined properly as well as effectively along with other ground-based and sat-ellite measurements of major ionospheric parameters.

Figure 1. A sequence of 12 consecutive auroral images taken from the DE 1 spacecraft, dis-playing global auroral activity at ultraviolet wavelengths. [Courtesy of L. A. Frank]

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2. Auroras

2.1. Auroras from spaceThe aurora, one of the dominant manifestations of the magnetospheric sub-

storm, is perhaps the most fascinating and captivating majestic natural phenome-non to be seen on the earth’s surface, although unfortunately this impressivemulti-color display can be observed regularly only by a limited number of peopleliving near the polar regions. Anyone who has ever witnessed the display of infi-nite shapes and movements of the aurora in the entire sky knows that the wholedrama can never be described with adequate vocabulary invented by human being.The aurora appears as a tremendous spectacle in the dark sky, with structureddisplays moving rapidly but erratically in all directions, changing the combinationof color.

The aurora has continuously been a subject of curiosity for space physicists aswell as for the natives living at high latitudes. Not until recently was it welldocumented that the aurora on a global scale behaves in a well-defined, system-atic manner, with characteristic features that recur under similar conditions interms of the degree to which the solar wind interacts with the magnetosphere[Akasofu, 1964, 1977]. It has become possible, with the imaging capability ofseveral polar-orbiting spacecraft, to monitor nearly the entire auroral displaysfrom above the northern and southern poles, so that we are beginning to use ex-tensively spacecraft images to construct a relatively complete picture of auroralphysics [e.g., Anger et al., 1973; Frank et al., 1988; Craven and Frank, 1991].Figure 1 shows a sequence of 12 consecutive auroral images taken from the Dy-namics Explorer 1 satellite, from over the northern polar region. It is noticed thata brightening of auroras occurred in the midnight sector [at the fourth image atupper right] and proceeded eastward and westward, as well as poleward, with themaximum epoch by the sixth and seventh frames.

0

80°

70°

60°

12

1880

°70

°60

°

0

12

Q = 0 Q = 1

0680

°70

°60

°

0

12

0

80°

70°

60°

12

Q = 4 Q = 7

Figure 2. Auroral oval determined by Feldstein and Starkov [1967] in geomagnetic coordi-nates. To show the relative location of the auroral belts, the geomagnetic Q index is referredto.

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90

80

70

60

0

LTENGA

CI ACOL

Location of Equatotward Boundary

22

of Auroral Oval

Bz = - 5 nTBz = 5 nT

21

20

Bz = 0

23M

E ( hours)IT M

INVARIANT LATITUDE (degrees)

2

1

3

4

Figure 3. Location of the equatorward boundary of the diffuse electron precipitation at differ-ent local times [in MLT] in the dark sector for three Bz values of the IMF. After Kamide andWinningham [1977].

2.2. The auroral ovalIf one looks at our planet, the earth, from space, it has two annular rings-shaped

glows, one surrounding the north and the other surrounding the south polar re-gions. These annular belts of auroral luminosities are often called the auroralovals. The auroral oval delineates approximately the area called the polar cap,where geomagnetic field lines are “open,” being connected to the interplanetarymagnetic field [IMF].

The size of the auroral oval changes considerably with geomagnetic activity:see Figure 2. The “classical” auroral oval [or belt], which is defined statisticallyas the locus of high frequency [≥ 75%] of auroral appearance [Feldstein, 1966],has been used extensively to order geophysical phenomena. The size of the auro-ral oval is not fixed in space but varies with magnetic activity. During activeperiods the classical auroral oval expands equatorward, reaching the latitude ofthe auroral zone, while it contracts poleward during periods of low geomagneticactivity [Feldstein and Starkov, 1967]. Meng et al. [1977] showed that the globalauroral distributions indeed are close to the shape of an off-centered circle, in-stead of the oval shape, during extremely quiet periods.

A southward IMF results in a net magnetic flux transfer from the dayside to thenightside, causing the equatorward shift of the auroral oval [Cowley, 1982]. Anextensive study of auroral motions indicated that the north-south component ofthe IMF controls the size of the auroral oval, although there is a difficulty inexamining whether its location depends solely on the IMF or on both the IMF andgeomagnetic activity because of the existence of the close statistical relationshipbetween the southward IMF and geomagnetic disturbances.

191

Equ

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war

d B

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o f A

uror

al O

val

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(mV/m)

70

at M

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nig h

t (d

egre

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)

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MAX

2

B sV

3

72

5 6

Figure 4. Location of the equatorward boundary of the auroral oval plotted agaist the maxi-mum 30-min average Bz V value during six hours preceding the time of each auroral obser-

vation. After Nakai and Kamide [1983].

In addition to visual auroras, we may be able to use several other measurableparameters to quantify the size of the auroral oval. One of them is electron pre-cipitation observed by polar orbiting satellites. Figure 3 shows the average loca-tion of the equatorward boundary of the “diffuse” precipitation for three differentIMF Bz values. It is clearly seen that the IMF dependence of the oval location inthe morning sector is stronger than that in the evening sector. When the Bz valuedecreases from 5 nT to –5 nT, the boundary tends to move equatorward by 8degrees in the morning sector while only 5 degrees in the evening sector [Kamideet al., 1977]. Assuming that the diffuse electrons in the auroral oval originate inthe inner boundary of the plasma sheet, this local time dependence of the auroraloval may be accounted for by the low-energy plasma motion in the magnetotail inwhich a large-scale uniform electric field is superposed on the corotation electricfield.

The importance of the delineation of the auroral oval boundaries lies not onlyin auroral morphology at the ionospheric level but also in dynamic processes inthe magnetosphere. It is generally accepted that the Bz component of the IMF isthe important factor that does control the size of the average oval, but correlationcoefficients of the nightside auroral oval with 1-hr average Bz are rather low,falling between 0.4 and 0.7, indicating that the auroral oval does not always fol-low the IMF Bz variations in a linear form. Nakai and Kamide [1983] tried todetermine the most probable time scale of the auroral oval response to IMF varia-tions. Aurora imagery data with high time resolution were used in such a way that

192

the maximum value of 30-min average Bz V during several hours preceding eachof the satellite pass is calculated. It was found that this simple parameter corre-lates well with the oval location and the correlation tends to be improved gradu-ally as the time scale becomes larger. Figure 4 shows the latitude of the ovalboundary against the maximum Bz V during six hours preceding each satellite passtime. It is noticeable, however, that the relationship between the oval size and themaximum Bz V is well represented by a curved line, indicating that the rate of theoval expansion at larger Bz values becomes lower.

Figure 5. Schematic diagram showing the main characteristics of auroras for the averagedisturbed condition. Discrete auroral arcs are indicated by solid lines and the diffuse auroralregions are shaded. After Akasofu [1976].

2.3. The auroral substorm as a manifestation of magneto-sphere-ionosphere coupling

What is an auroral substorm? An auroral substorm occurs primarily in the auro-ral oval. The term substorm originally entered the vocabulary of the space physi-cist through a study of the dynamics of discrete auroral forms [Akasofu, 1964]. Itwas found that the development of highly dynamic auroral forms follows a re-peatable pattern, serving a framework in which a variety of observations of parti-cles and fields in the high-latitude ionosphere are properly ordered. The auroralsubstorm involves a brightening of auroral arc forms in the midnight sector with

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the subsequent poleward motion which is accompanied by a specific type of auro-ral display called the westward traveling surge. The earth’s magnetic field under-goes a considerable perturbation, particularly at high latitudes, during the auroralsubstorm. This is called the polar magnetic substorm.

Figure 5 shows the main characteristics of auroras during auroral substorms, inwhich there are essentially two auroral belts, diffuse and discrete auroras [Aka-sofu, 1976]. The diffuse aurora can be defined as a broad band of structurelessauroral luminosity with a latitudinal width of, at least, several tens of kilometerswhich is separated from the discrete aurora. The diffuse aurora often covers asignificant part of the field of view of an all-sky camera, making it difficult torecognize its presence from a single ground station. Thus, the auroral oval definedby Feldstein and Starkov [1967] using all-sky camera data does not necessarilyrepresent accurately the distribution of the diffuse aurora. This character of thediffuse aurora contrasts in many ways with that of the discrete aurora. The dis-crete aurora is a curtain-like structure and considerably variable in its morpho-logical features and energy spectra of its precipitating energetic electrons.

3. The Solar Wind and Substorms

3.1. Solar wind-magnetosphere dynamoThe solar wind is an ionized gas, flowing continuously from the solar corona

and filling up the interplanetary space. As the solar wind, which carries the solarmagnetic field, interacts with the earth’s magnetosphere, as much as several 106

MW of power is generated through a dynamo process. The efficiency of the dy-namo action depends on the relative orientation of the solar wind’s magnetic field,i.e., the IMF, and the earth’s magnetic field. This process is basically the same asthat of an MHD generator.

The generated energy through the natural power plant is partially discharged andeventually dissipated in the polar ionosphere through such a non-linear plasmaprocesses as substorms. The discharge process produces a great variety of phe-nomena in the magnetosphere and the ionosphere: see Kamide and Baumjohann[1993] for details. The aurora substorm is one of the manifestations.

If the ionosphere does not exist at all, we would not expect much: see Section 5for the characteristics of the ionosphere. A number of exciting phenomena, such asauroral displays, occur because the energy from the solar wind-magnetospheredynamo is transmitted mainly to the nightside ionosphere through the magnetotail.It is also important to note that the ionosphere is not merely a passive load, but itdoes constitute a complex feedback system with the magnetosphere. The amountof energy released in the high-latitude ionosphere during a single substorm is infact negligibly small, compared to the free energy available in the magnetosphere

194

which is powered from the solar wind-magnetosphere dynamo. It is thereforepossible to assume that substorms are a random process that occurs any timeregardless of the amount of the energy that the magnetosphere-ionosphere systemgains from the solar wind.

Studies have shown, however, that substorms do not occur at random but themagnetosphere is a rather efficient system in both extracting the solar wind energyand converting the extracted energy into the substorm energy on such a rathershort timescale as a few hours. The magnitude and the location of substorms, aswell as the probability of substorm occurrence are all correlated well with thedegree to which the magnetosphere couples with the solar wind.

3.2. Substorm intensityThe magnitude of substorms, in terms of the total current of the auroral elec-

trojets, has been shown to be correlated with the southward component of theIMF. The total electrojet, thus the energy of substorms dissipated in the polarionosphere, is more intense when the IMF is more southward directed. The mag-netosphere reaches the “ground” state only during a prolonged period of a largepositive Bz value, and under such a condition the auroral oval contracts to itsminimum size. The midday and midnight portions of the auroral oval contract toinvariant latitudes of 81-82º and 72-73º, respectively. The total area of the mini-mum size of the polar cap which is surrounded by the auroral oval is approxi-mately 7.5 106 km2.

Bz N-S Component of IMF

–4

6

Tot

al C

urre

nt o

f Wes

twar

d E

lect

roje

t

2

1

3

4

5

amp

)

10

7

8

9

5

Northward4 2 0 –2

low lat.

∆

∆

Southward

5

–6 –8

H

H

∆H

nT

10

10

5 nT

–10

Figure 6. Dependence of the intensity of the total westward auroral electrojet on the north-south component of the interplanetary magnetic field for different values of mid-latitude posi-tive H perturbations [indicated by different symbols]. After Kamide and Akasofu [1974].

195

80

5am

p )

Tot

al C

urr e

nt o

f Wes

twar

d E

lect

roje

t

Geomagnetic Latitude (degrees)

5

0.90.8

0.7

60

2

1.5

1

4

3

65

6

7

1098

70 75

-3 Bzuncertain

Bz 0 nT0 Bz -3

Figure 7. Location and the total current intensity of the auroral electrojet during the maxi-mum phase of substorms for different values of the IMF Bz component [indicated by differentsymbols]. After Kamide and Akasofu [1974].

(Southward)

Pro

babi

lity

( %

)

1 - HR Average IMF Bz (nT)

"Substorm Time"

(Northward)410

0

50

8 6 2 0 –2 –4 –6

"Quiet Time"

100

–8 –10

Figure 8. Probability of substorm time [represented by the heavy line] and quiet time [by thelight line] as a function of the Bz value of the IMF. After Kamide et al. [1977].

196

On the basis of a detailed examination of the latitudinal dependence of elec-trojet intensity, Kamide and Akasofu [1974] discussed the magnitude of sub-storms in terms of the total current of the westward auroral electrojet. The cor-responding north-south polarity of the IMF and mid-latitude geomagnetic per-turbations were also examined. Figure 6 shows the statistical relationship be-tween the total current of the westward electrojet and the Bz value of the IMF.Average Bz values during the hour preceding the maximum phase of substormswere used. It can be seen that for substorms associated with a northward IMFand a southward IMF of small magnitudes [less than approximately 3 nT], theintensity of the total westward electrojet is small [at most 4. 105 A]. The onlyexception [the bracketed circle] in Figure 6 occurred during a magnetic storm.

3.3. Location of substorm occurrenceThe location of the substorm expansion onset is also controlled by the polar-

ity of the IMF: substorms occur at higher latitudes when the IMF is less south-ward-directed. Figure 7 shows the latitude of the electrojet center during themaximum phase of substorms as a function of the total current intensity; thehalf widths [which are different on the equatorward and poleward sides of thecenter] of the electrojet are also shown by a horizontal line. It is clear that theregion of the electrojet shifts systematically equatorward as the total current in-tensity increases; an increase in substorm intensity from 105 to 106 A in the to-tal current intensity is associated with an equatorward shift from 70º to 65º.There is also a tendency for the latitudinal width of the electrojet to increase forgreater values of the current intensity.

One interesting feature is that weak substorms, regardless of whether they areassociated with a positive Bz or a weak negative Bz of the IMF, tend to occuralong the contracted auroral oval at higher latitudes. Such small, yet important,substorms cannot be detected without, at least, several meridian chains of sta-tions. In terms of the total electrojet current intensity, the intensity of substormsranges from less than 105 A to more than 106 A. Since Joule heating of theauroral electrojet is a significant part of substorm energy dissipated in the polarionosphere, it is important to note that there is a difference of more than 102 inthe amount of dissipated energy between weak and intense substorms [Baumjo-hann and Kamide, 1984; Lu et al., 1995]. This means that the parameters thatcontrol the total energy of substorms must have a similar dynamic range. It isconceivable that the magnetic field intensity B or energy B2/8π at the location ofthe substorm origin in the magnetotail is an important factor in determining thesubstorm intensity, since weaker substorms tend to occur at higher latitudes andthus at greater geocentric distances than stronger substorms.

197

3.4. Probability of substorm occurrenceThere is one important problem which is crucial in seeking substorm genera-

tion mechanisms [see, for example, McPherron, 1970; Lui, 1991; Lyons, 1995].Does substorm occurrence probability depend on the Bz component of the IMF[or equivalently on the size of the auroral oval]? If the occurrence frequencyhas a strong dependence on the IMF direction, it is reasonable to state that theoccurrence frequency of substorms is closely related to the amount of energystored in the magnetotail, since there is a definite relationship between the IMFBz and the magnetic energy stored in the magnetotail [e.g., Fairfeild and Lep-ping, 1981]. If, on the contrary, the occurrence probability has no such depend-ence, substorms may be regarded as a random process. This dependence wasdifficult to examine critically because of the lack of continuous observationaldata on the entire polar region.

Lui et al. [1975] have shown that the substorm “seeing” probability decreasesas the auroral oval size decreases. It was then suggested that although the seeingprobability is not the same as the occurrence probability, there is the possibilitythat the latter decreases as the auroral oval contracts poleward.

Figure 8 shows the frequency [probability] of observing substorms as well asquiet times as a function of the IMF Bz [Kamide et al., 1977]. The probability

P [in percent] was computed as P = S / T × 100, where S is the number of sub-storm events in every 1 nT interval of Bz and T is the total number of the sam-ples in the same Bz interval. The substorm probability presented in Figure 8 isthe probability of a substorm observation with electron spectra by polar-orbitingsatellites, ISIS 1 and 2. It is seen that the substorm probability increases as Bz

decreases; however, this increase does not occur in a simple way. In the rangeBz ≥ 2 nT the probability is almost constant at the 20-30% level. It then increasemonotonically for greater southward IMF, and if the magnitude of the south-ward Bz is larger than 5 nT, the substorm probability becomes essentially 100%.

This statistical result somewhat restricts our options in seeking generationmechanisms for magnetospheric substorms. Figure 8 clearly shows that sub-storms do not occur with an equal probability for different values of the IMF Bz

component for different sizes of the auroral oval. Since the magnetospheric sub-storm can be considered a process by which the magnetosphere tends to removesporadically the excess energy in the magnetotail, the substorm occurrenceprobability is closely related to the amount of energy stored in the magnetotail.This implies that the triggering mechanism has something to do with an increasein the stored energy. In what way? We do not have, at present, a satisfactoryanswer to this simple question.

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Figure 9. [a] Schematic diagram of auroral features during a typical auroral substorm. [b]Distribution of equivalent current vectors with reference to the auroral features shown in [a].The magnitude of each current vector is normalized for the maximum magnitude of the mag-netic perturbation of 500 nT. After Kamide and Akasofu [1975].

4. The Auroral ElectrojetsFigure 9 shows a nightside half of Figure 5, which is a schematic diagram of

auroral characteristic features. In order to identify global auroral behavior withhigh-latitude ionospheric currents, the distribution of equivalent current vectors[see Kroehl and Richmond, 1977 for details on the practical procedure of calcu-lating the equivalent current function] is plotted for the maximum phase of sub-storms. It is clear that the current flow at high latitudes is concentrated in theauroral oval, forming the auroral electrojets. The auroral electrojets are the mostprominent current flow at high latitudes.

The term “auroral electrojet” was used originally to describe a specific class ofcurrent configuration in which spatially concentrated currents flow at aurorallatitude. How and how much concentrated is not defined quantitatively, but thereis no doubt that the concentration of the current flow has a close connection withauroral displays, particularly with the discrete aurora. In fact, in the past, it hasbeen tacitly assumed that the auroral electrojets are most intense in the region ofbright auroral luminosity. Is this really the case?

It is legitimate to assume that precipitating auroral electrons are responsible foractive auroral displays and, at the same time, for enhancing the rate of ionizationof the upper atmosphere and the ionospheric conductivity, thus increasing theionospheric currents. There is no a priori guarantee, however, that the corres-

199

Eastward

Discontinuity

Midnight

Westward

During Non-Substorm Periods

Harang

Eastward

Westward

Midnight

Harang

Discontinuity

During Substorms

Figure 10. Sketch of the auroral electrojets during substorms [right] and during non-substorm times [left].

ponding electric field is unchanged in the auroral region when intense auroralprecipitation occurs during substorms.

Figure 10 shows schematic illustrations of the auroral electrojets, eastward andwestward, for relatively quiet periods and for disturbed times. The so-called Ha-rang discontinuity region is defined by the boundary region between the twoelectrojets, or the boundary between the regions of northward and southwardelectric fields. One of the differences between substorm and non-substorm timeslies in the local time of the Harang discontinuity. During substorms, the westwardelectrojet penetrates deep into the evening sector through the midnight sector.Typical values of ionospheric electric fields and conductivities for the two condi-tions are listed in Table 1, where high degree of variability in these parameters isnoted, depending upon the intensity of substorms and even on the substormphases during a single substorm.

During Nonsubstorm Times

Eastward Electrojet Westward Electrojet

Center of Electrojet Near 1800 MLT Near 0600 MLT

Electric Field [E] 20-50 mV.m-1 [Northward] 0-20 mV.m-1 [Southward]Pedersen Conductivity [ΣP] 2-5 S 2-5 SHall Conductivity [ΣH] 2-5 S 2-10 S

During Substorms

Eastward Electrojet Westward Electrojet

Center of Electrojet Near 1800 MLT Anywhere in the dark sectorElectric Field [E] 20-50 mV.m-1 [Northward] 0-100 mV.m-1 [Southward]Pedersen Conductivity [ΣP] 5-10 S 10-20 SHall Conductivity [ΣH] 5-10 S 20-50 S

Table 1. Typical values of ionospheric conductivities and electric fields during substorms andnonsubstorm times

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N

ail Current

S

Electrojet

Near EarthNeutral Line

TailAxis

Field-aligned Currents

Figure 11. The diversion or disruption of the tail current through the ionosphere during thesubstorm expansion phase. After McPherron [1991].

During substorms, the ionospheric current flow is affected essentially in twoways to accommodate the enhanced energy input from the solar wind via in-creased dissipation: see Baumjohann and Treumann [1996]. On one hand, thecurrent flow in the “convection” auroral electrojets increases directly relating tothe energy input from the solar wind along with the directly-driven process insolar wind-magnetosphere interactions [see Akasofu, 1981; Baker et al., 1985;Rostoker et al., 1983; Pellinen, 1993]. On the other hand, the solar wind energywhich is not directly dissipated via enhanced convection in the auroral electrojetsis stored once in the magnetotail, mainly in the form of magnetic energy by en-hancing the neutral sheet current. This is accomplished by a significant distortionof the nightside magnetospheric field lines into a tail-like configuration even atsmall radial distances where the field is basically dipolar. After some 30-min.long phase of energy storage, the magnetic tension is suddenly released at expan-sion phase onset. This is equivalent to the partial disruption of the tail current,generating short-circuiting the neutral sheet current in an azimuthally limitedregion of the tail and diverting its current along magnetic field lines and throughthe auroral ionosphere in the midnight sector [McPherron et al., 1973]. Suddenrelease of energy which has previously been stored in the magnetotail leads to theformation of the so-called substorm current wedge with enhanced westward cur-rent flow in the midnight ionosphere: see Figure 11 [McPherron, 1991].

What leads to the short-circuiting of the neutral sheet current and the formationof the substorm current wedge is to be unveiled in future studies. The substormcurrent wedge expands both poleward and westward during the course of the ex

201

Ionosphericcurrent

Field-alignedcurrent

Tail current

c

Sun

c’

b’

b

dd’ a

a’d’

a

r

d

ar ati l

Pc

c’

entrring cu

b’

b

a’

Sun

Figure 12. [a] Model current system for polar substorms. The dotted area represents the re-gion of the westward electrojet. [b] Schematic illustration of the three-dimensional currentsystem for magnetospheric substorms. After Kamide et al. [1976].

pansion phase. Its western edge is always collocated with the head of the west-ward traveling surge, a unique auroral form typically associated with the substormexpansion phase [Meng et al., 1978; Baumjohann et al., 1981]. The detailedstructure of ionospheric electric fields, conductances, and ionospheric and field-aligned currents in the substorm-disturbed region, especially near the head of thesurge, can be unfolded by incoherernt-scatter radars [see, for example, Banks andDoupnik, 1975; de la Beaujardiere et al., 1977].

A diversion of a fraction of the cross-tail current occurs along field lines to theionosphere, within which the current flow is westward; see Figure 11. How is thecurrent distributed in the auroral ionosphere? Figure 12 summarizes the vastamount of Chatanika radar observations [Brekke et al., 1974], showing an empiri-cal model of the three-dimensional current system for substorms [Kamide et al.,1976]. The westward electrojet, which is one of the dominant manifestations ofsubstorms, is fed by the field-aligned currents in a manner suggested by thewedge current model, but a significant part of the downward field-aligned cur-rents in the morning sector flows southward, and then flows out of the ionosphereas the upward currents.

It is evident that the current pattern is much more complicated in the eveningsector than in the morning sector. There are downward field-aligned currents inthe area of the eastward electrojet. The intense upward currents are connectedwith the westward electrojet in the premidnight sector and also with the northwardionosphere current, which is eventually connected to the inward field-alignedcurrents through the eastward electrojet. Thus, the integrated intensity of theupward field-aligned currents is much more intense than that of the downward

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currents, showing the existence of a net field-aligned current [e.g., Iijima andPotemra, 1976]. This is consistent with the observations made by polar-orbitingsatellites and with the inference from ground magnetic perturbations at mid-latitudes. This current configuration is also in good agreement with radar obser-vations which show that the northward ionospheric current prevails in the eveningsector [Horwitz et al., 1978]. It is indicated that the eastward electrojet flowsnortheastward as it approaches the midnight sector and eventually connects to thewestward electrojet in the Harang discontinuity region.

Without early observations by the Chatanika radar, it would have not been pos-sible to reach such a realistic three-dimensional current system. Multi-radar stud-ies from the EISCAT KST (Kiruna-Sodankilä-Tromsö) and ESR (EISCAT-Svarbard) radars are capable of making clear the changes of this system at differ-ent substorm phases. It should be noted that the global current patterns changequite dramatically in association with substorm times, or with the substorm phases[Kamide and Kroehl, 1994; Kamide et al., 1996]. Thus, to understand the energyflow from the solar wind through the magnetosphere to the ionosphere on anindividual bases, it is essential to describe details of temporal variations of thesubstorm current system before and during the substorms. This problem relatesclosely to the major question of the magnetospheric substorm and in particular tothe evaluation of the relative importance of two energy dissipation mechanisms:the “directly driven” and “unloading” processes [Akasofu, 1981], both of whichhave been proposed as playing an essential role in magnetospheric substorms.

5. Ionospheric Electrodynamics During Substorms:Radar Measurements

The ionosphere is produced primarily by the ionizing action of ultraviolet ra-diation from the sun and auroral energetic particles that strike the upper atmos-phere. Electric currents flow throughout the ionosphere and are strongly influ-enced by the presence of the earth’s magnetic field. The motions of the iono-spheric particles are affected by collisional interaction with upper-atmosphericparticles, as well as by electric fields extended into the magnetosphere. In otherwords, the ionosphere is the physical link between the magnetosphere and theneutral atmosphere [Killeen et al., 1985]. In particular, the polar ionosphere is adynamic region, playing a key role in our understanding of the most fundamentalplasma process, the substorm, occurring in the magnetosphere-ionosphere cou-pling system [e.g., Foster et al., 1986]. It is the region where beams of auroralprecipitation collide with atoms and molecules, ionizing and exciting them. Auro-ras result, intense electrojet currents flow, and a significant amount of heating isgenerated: see Section 2.

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C 1411 - 1423 UT July 7, 1978

y

Invariant Latitude ( degrees )

Chatanika

-0.5

-200Gro

und

Mag

netic

Per

turb

atio

n (n

T)

-300

0

-100

100

6362 64

20

Con

duct

ivity

(mho

)D

ensi

ty (A

/m)

Iono

sphe

ric

Cur

rent

0

0.5

0

(mV

/ m

)E

lect

ric

Fie

ld

-80

4060

-120

-400

40

j

jx

yNorth

x East

6765x

66

'H

'Z

68

6 P

6 H

Ey

Ex

Figure 13. Latitudinal profiles of the electric field, height-integrated conductivity, and iono-spheric current, and the corresponding magnetic perturbations for the morning sector. AfterKamide and Vickrey [1983].

There has been a growing realization that the polar ionosphere plays a principalrole in large-scale magnetospheric processes; however, spatial/temporal variationsin electric fields and currents have proved to be extremely complicated. Towardunderstanding of such complicated observations under various substorm condi-tions in terms of the basic assumptions that lead to reproducing the main featuresof observed phenomena, incoherent scatter radars are capable of examining manydifferent parameters in the ionosphere [see Schlegel, 1996; Richmond, 1996].These parameters obtained by the radars during the different phases of substormscan then be compared with satellite measurements of electric fields and currentsas well as with simulation studies in which the corresponding parameters can bechanged to a realistic degree to demonstrate how the basic equations/assumptionsare able to reproduce the key character of radar observations.

To address the question of whether it is the changes in the conductivity or inthe electric field that are most important in producing enhanced currents, i.e., theauroral electrojets, in different regions of the polar ionosphere, it is then essentialto be able to measure more than one ionospheric parameter simultaneously atmore than one site. One of the merits of the operation of coherent scatter radars isthat in certain modes of operation, the radar beam can probe the altitude/latitudedistribution of electron density and line of sight plasma drifts from which theelectric fields, conductivities, and currents in the ionosphere can be determined[see Robinson et al., 1985].

204

E

Magnetic Local Time

Harang Discontinuity

22

00

ElectrojetEastw

ard

E

18

20

Electric FieldDominant

WestwardConductivity

E02

Dominant

Electric FieldDominant

lect ro je t

E

04

06

Figure 14. Schematic diagram of the auroral electrojets showing different roles of electricfields and conductivities in the eastward and westward electrojets at different latitudes andlocal times.

In order to clarify the different roles of the conductivity and electric field in thedifferent electrojet regions, data from the Chatanika radar were used, examininghow they change over latitude during substorms [Kamide and Vickrey, 1983]. Thelatitude profile of the ionospheric current in the morning sector indicates, asshown in Figure 13, that the westward electrojet was flowing in the region be-tween 63° and 68°, having a northward [southward] component in the equator-ward [poleward] half of the electrojet. An interesting feature of this latitudinalprofile is that in the equatorward half of the westward electrojet, the conductivitywas high while the electric field was small. The situation tended to be reversed inthe poleward half, where the southward electric field was very intense but theconductivities dropped drastically. This characteristic implies that bright aurorasand the corresponding energetic electron precipitation were present only in theequatorward half of the morning westward electrojet. The center of the electrojetseemed to be located in the region sandwiched by two peaks in the southwardelectric field and the conductivity.

The ratio between the Hall conductivity and the electric field has also been ex-amined as a function of magnetic local time. If we use commonly adopted units, Sand mV/m, respectively, their average ratio for the eastward electrojet is found tobe less than 0.5, whereas that for the midnight sector westward electrojet before03:00 MLT is close to 4. The Hall conductivity of the midnight sector westwardelectrojet is sometimes 15 times greater than that in the eastward electrojet.

In the region of the eastward electrojet in the evening sector, the northwardelectric field is the main contributor to the magnitude of electrojet current, in thesense that the field magnitude is greater, compared to the southward field magni-

205

tude in the westward electrojet. Another point of interest is that there are essen-tially two modes to the westward electrojet: one in which the contributions to theelectrojet magnitude are “conductivity dominant” and the other “electric fielddominant.” The exact classification into these two modes of the westward elec-trojet using observed data is difficult, if not impossible, because the correspond-ing currents are contiguous everywhere. The substorm westward electrojet nearmidnight is characterized mainly by the relatively high Hall conductivity, whereasthe westward electrojet in the morning sector is dominated by the large southwardelectric field.

Figure 14 summarizes these characteristics quite nicely. The boundary betweenthe conductivity dominant and electric field dominant westward electrojets is notas clear in reality as is indicated in Figure 14. However, an important point is that,although it has been a common practice to assume that the westward electrojet isassociated during substorms with a conductivity enhancement, a part of the west-ward electrojet in the later morning sector can be intensified without having highconductivity values. In particular, the latitudinal profile of the westward electrojetin the early morning sector [01:00-03:00 MLT] would indicate that its polewardportion has a relatively strong southward electric field while its equatorwardportion has a relatively high Hall conductivity.

It is of great importance to investigate further whether the eastward electrojet inthe evening sector and the westward electrojet in the late morning sector in Figure14 may be driven by a voltage source in the magnetosphere, while the substormwestward electrojet in the midnight sector is supplied from a current source by,for example, the disruption of portions of the magnetotail currents. It has alreadybeen shown that there are basically two types of current systems: DP 1 and DP 2[Nishida and Kokubun, 1971; Baumjohann, 1983]. Clauer and Kamide [1985]indicated that these two modes can coexist at all times during disturbed periodsand the relative strength of these currents varies from time to time, making indi-vidual current patterns very complex. Furthermore, the pattern of “enhanced” DP2 has been shown to appear throughout substorm activity: see, for example, Shueand Weimer [1994]. Note that Figure14 supports the idea that the conventionalDP 2 currents are governed by electric field enhancements while the substorm DP1 currents are mainly caused by strong conductivity increases, accompanying thebreakup auroras.

It is important to realize that on days with nearly persistent energy input fromthe solar wind, both processes are typically operating at the same time. It is con-ceivable that this is the reason why substorm signatures, such as the distributionof magnetic perturbations vectors and electric fields and its time changes, arequite complicated. Although it has long been argued that certain substorm-

206

associated phenomena are consistent or inconsistent with either the directly-driven process or the loading-unloading process, one could resolve such confu-sion by realizing that the magnetospheric substorm involves the two processessimultaneously. As demonstrated in Kamide and Kokubun [1996], coordinatedradar observations with spacecraft will increase the potential of understanding therelative importance of the two processes during the different phases of substorms.

6. Modeling of Electric Fields and Currents in the PolarIonosphere

6.1. Basic EquationsThe active role of the polar ionosphere is to link the magnetospheric plasma

and the neutrals in the thermosphere. The self-consistent chain for the entiremagnetosphere-ionosphere coupling system represents a closed loop consisting ofa number of individual links [see Figure 15, Vasyliunas, 1970]. Studies of theo-retical models, which are intended to examine the entire loop, and those intendedto aid in the understanding of “local” chains, or individual links, must be com-plementary to each other. It is in the local regions where remarkable energy con-version processes such as substorms are taking place. It is important to realize thatalthough incoherent-scatter radars are a powerful tool with which to sense theelectrodynamic state of the ionosphere, they also provide us with essentially

Kinetic

Equation

Boundary Source

Pressure

Particle

ConservationMomentum

Electric Field

Magnetospheric

GeneralizedOhm’s Law

Field - Aligned

Perpendicular

of Current

Continuity

Current

Current

IonospheriOhm’s Law

Driving Field (or Current)

Electric Field

Ionospheric

Figure 15. Logic diagram for a self-consistent calculation of magnetosphere-ionosphere cou-pling associated with magnetospheric convection. Each line joining two adjacent boxes islabeled with the physical principle or equation that links the two physical quantities. AfterVasyliunas [1970].

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“point” measurements. The radar measurements need to be comple-mented/normalized by numerical simulations of the entire chain of processes. Thissection presents the basic equations for simple models with special emphasisplaced on ionospheric electrodynamic processes. It attempts to obtain a set ofnumerical solutions to the equations governing the magnetosphere-ionospheresystem in such a way as to include far less idealization or simplification by refer-ring to more essential observational characteristics than would be required forpure theories. In this way, it is possible to demonstrate how the basic assumptionslead to the main signatures in the high-latitude ionosphere, as observed by inco-herent-scatter radars.

In order to simplify conditions, a number of assumptions are made throughoutthe entire calculation process. The most important and crucial assumptions weemploy are as follows:

[1] The ionosphere is regarded as a two-dimensional spherical current sheet witha height-integrated layer conductivity.

[2] The earth’s magnetic field lines are taken to be equipotentials, neglectingparallel electric fields.

[3] Only steady-state solutions are considered.The continuity equation for electric currents under these simplifying conditions

is expressed as

div J = j sin χ (1)

where J is the height-integrated ionospheric current density, j is the density ofthe field-aligned current [positive for a downward current], and χ is the inclina-tion angle of a geomagnetic field line with respect to the horizontal ionosphere.Ohm’s law for the ionospheric current is written as

J = E = – Φ (2)

where E and Φ are the electric field and the corresponding electrostatic potential,respectively, in the frame rotating with the earth, and is the dyadic of the height-integrated ionospheric conductivity. The combination of Eqs. (1) and (2)yields

. [ Φ ] = – j sin χ (3)

which is to be solved for Φ under suitable boundary conditions. The boundaryconditions we employ can be:

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180 °

Electric Potential

0.0

-32.0

= 90 °

= 8 kV= 0 °

30 °60 °

Figure 16. Electric potential distribution [8-kV contour interval] over the northern hemi-sphere for a typical medium-size substorm. After Kamide and Matsushita [1979].

Φ = 0 (at the poles) ∂ Φ ∂ θ

= 0 (at the equator) (4)

where θ is the colatitude. As long as we concentrate on the high-latitude iono-sphere [say, θ ≤ 30º] , the boundary conditions are not very important. In solstitialseasons, however, an asymmetry in the ionospheric conductivity between thenorthern and southern hemispheres is present, and hence the resultant electriccurrents are also expected to be asymmetric. In such cases, actual calculations aremade for both the northern and southern hemisphere, depending on the season.

Given a specific conductivity model and an assumption about the field-alignedcurrent distribution, one can solve Eq. (3) to find the electric potential Φ in thehigh-latitude ionosphere. The differential equation corresponding to Eq. (3) issolved numerically to obtain the most probable potential value at each of the gridpoints in the scheme. By using the [θ, λ] coordinate system, in which θ is colati-tude and λ is longitude, measured eastward from midnight, Eq. (3) can be reducedto the form

209

A ∂ 2 Φ ∂ θ 2 + B

∂ Φ ∂ θ

+ C ∂ 2 Φ ∂ λ 2

+ D ∂ Φ ∂ λ

= F (5)

where

A = sin2 θ Σθθ , D = sin θ ∂ Σθ λ

∂ θ +

∂ Σ λλ∂ λ

,

B = sin θ [∂ sin ( θ Σθθ )

∂ θ – ∂ Σθλ ∂ λ ], F = –a2 j sin2θ sin χ,

C = Σλλ , sin χ = 2 cos θ

(1 + 3 cos2 θ )1/2 ,

and a is the radius of the current sheet. Note that if all the conductivity gradientsare neglected Eq. (5) is reduced to the Poisson equation. Further, in the regionwhere j = 0, the Laplace equation is obtained.

The component of the height-integrated ionospheric current J is given by

Jθ

Jλ =

Σθθ Σθλ

– Σθλ Σλλ

Eθ

Eλ (6)

where the electric field component is expressed as:

Eθ = – ∂ Φ

a ∂ θ , Eλ = –

∂ Φ a sin θ ∂ λ (7)

6.2. Typical substormA model calculation for a “typical” substorm is presented. Note that actual

substorms exhibit highly variable processes in the magnetosphere-ionospheresystem. Based on models of the average distribution of the ionospheric conduc-tivities and of field-aligned currents derived from radar and satellite observations,the electric potential is solved [see Kamide and Matsushita, 1979]. Figure 16shows the result. If the potential at the pole is assumed to be zero as one of theboundary conditions, the highest and lowest potential values are 88 and -40 kV,respectively. The large difference between the magnitudes of these values indi-cates how strongly the conductivity gradients [both in the background day-nightgradient and in the auroral oval] influence the overall potential distribution.There is also a considerable distortion of the equipotential contours within thenightside conductivity inhomogeneity, which produces an accumulation of thespace charges. A comparison of this potential pattern for the typical substormmodel with the pattern for quiet periods [not shown here] shows how intenseauroral enhancements can change the pattern of equipotential contours. For ex-ample, the potential centers undergo a significant shift from quiet periods to sub-

210

storms; the high potential contours move toward midnight, while the low contoursmove away from midnight.

The distribution of the ionospheric current vectors [not shown here] indicatesthe following important features:

[1] The eastward electrojet flows in the equatorward half of the evening auroralbelt, while the westward electrojet flows in wider regions in the evening andmorning sectors.

[2] The main part of these electrojets is supplied by the assumed field-alignedcurrents, because the ionospheric current in the polar cap and mid-latitudes isvery small.

[3] The westward electrojet appears to have two peaks, one at premidnight andone in the early morning hours. The maximum current density of the westwardelectrojet in the premidnight sector is produced primarily by the assumed highconductivity associated with a bright aurora. On the other hand, the westwardelectrojet in the morning sector occurs mainly as a result of the large electricfield there, although the contribution from the enhanced conductivity is notnegligible. The morning electrojet has a considerable southward component,which connects the downward field-aligned current [to the north] and the up-ward current [to the south] via the Pedersen current.

[4] The eastward electrojet is about one-third less intense than the westwardelectrojet.

[5] The eastward electrojet has a northward component, which becomes moreintense with the progress of local time; even a totally northward current is seenin the premidnight sector. This means that a significant fraction of the eastwardelectrojet turns northward and eventually joins the westward electrojet.

Kamide and Matsushita [1979] simulated the variability of the ionosphericelectric fields and currents in relation to the distribution of the field-aligned cur-rents, which varies considerably during magnetospheric substorms. Changes inseveral parameters to a realist degree of the typical substorm model have beenassumed. These changes are the result of intensity variations and locations shiftsfor field-aligned currents; effects of electric conductivity variations and seasonalchanges; and effects of additional field-aligned currents and an expanded auroraloval.

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7. The Role of Ground Magnetic Observations inAurora/Substorm Studies

7.1. The concept of magnetogram-inversion techniquesHistorically, ground-based magnetic records have been widely used to examine

physical processes occurring in the magnetosphere and the ionosphere, since themagnetic data obtained at the earth’s surface include valuable information about avariety of source currents flowing in the near-earth environment, including theionosphere and magnetosphere, the magnetopause, and the earth’s interior [seeNishida, 1978]. However, for that very reason, namely, that the data contain toomuch information, it has been a serious problem to evaluate the relative impor-tance of these currents in generating the particular patterns of global or localmagnetic perturbations that we are attempting to study [see Akasofu et al., 1980].

It is well known that in reality, ionospheric currents, such as the intense auroralelectrojets, are connected to field-aligned currents in a very complicated fashion,reflecting the variability of the degree of the magnetosphere-ionosphere couplingand causing a variety of different types and patterns of auroras and ground mag-netic perturbations. As pointed out by Potemra [1987], however, the debate be-tween Chapman and Birkeland concerning the existence of the field-aligned cur-rents continued until the mid-1960s [Zmuda et al., 1966], primarily because it isnot possible to determine uniquely the separate effects of ionospheric and field-aligned currents only from ground magnetometer observations, on which the paststudies have heavily relied.

Several computational techniques called the magnetogram-inversion methodshave been proposed; see reviews, for example, by Rees [1982], Kamide [1982],Feldstein and Levitin [1986], Glassmeier [1987], and Mishin [1990]. These nu-merical schemes are designed to compute not only the global distribution of bothionospheric and field-aligned currents, but also ionospheric electric fields and theJoule heating rate. Once we understand properly the origins of ground magneticperturbations in terms of various source currents, ground-based observations havean advantage over “more direct” measurements by radar and satellite, since varia-tions in the geomagnetic field are being monitored continuously at a relativelylarge number of fixed points on the earth’s surface. This contrasts with the intrin-sic ambiguity in determining the global three-dimensional current system on anindividual basis from single satellite passes, which have difficulties separatingtemporal and spatial changes.

This section describes the essence of the magnetogram-inversion scheme, alongwith its assumptions and limitations. Although several magnetogram-inversiontechniques start with the same set of basic equations, the practical procedures aswell as the points of emphasis vary considerably, depending on different

212

algorithms. The major algorithms [e.g., Fayermark, 1977; Mishin et al., 1979;Kamide et al., 1981] for obtaining the three-dimensional current system and iono-spheric electric fields require, first of all, that an ionospheric equivalent currentsystem can be adequately derived from an array of ground-based magnetic fieldmeasurements.

The equivalent current system is a toroidal horizontal sheet current JT assumedto be flowing in a shell at a 110-km altitude, whose associated magnetic fieldmatches the external portion of the observed magnetic variation field b. Thetoroidal current can be expressed in terms of an equivalent current function ψ. Inthe lower atmosphere, the magnetic variation can be expressed in terms of mag-netic potential V as

b = – V. (8)

With a given equivalent current function ψ and given conductivities, one isable to derive the ionospheric electric field, horizontal current, and field-alignedcurrent under the following simplifying assumptions:

[1] the electric field is electrostatic;[2] geomagnetic field lines are effective equipotentials, i.e., there is no “parallel”

electric field;[3] the dynamo effects of ionospheric winds can be neglected;[4] the magnetic contributions of magnetospheric ring currents, magnetopause

currents, and magnetotail currents to the equivalent current function can be ne-glected; and

[5] geomagnetic field lines are effectively radial.

The height-integrated horizontal ionospheric current J can be expressed as thesum of the toroidal [equivalent] current JP and a “potential” current JT as

J = JT + JP (9)

where the second component can be written in terms of a current potential τ. Thisis a special case of the well-known Helmholtz theorem for vector analysis. Thepotential component can be considered as a closing current for field-aligned cur-rents. The requirement that the three-dimensional current be divergence-freemeans that the field-aligned current density j [positive downward] satisfies therelation

j

= . J = . JP (10)

213

since JT is by definition divergence-free. The current system represented by j andJP together produces no ground magnetic variation under the assumption that thetoroidal component of J is just the equivalent current system.

Since the horizontal ionospheric current is related to the electric field E by

J = Σ E = ΣP E + ΣH E nr (11)

where ΣP and ΣH are the height-integrated Pedersen and Hall conductivities,respectively, Eq. (9) is then rewritten as

. Φ = – τ – nr (12)

where JP = – τ. A partial differential equation for the electrostatic potential

Φ in terms of ψ can be obtained by taking the curl of Eq. (12) as

[ nr] = ( . Φ ). (13)

The magnetogram-inversion technique requires knowledge of the height-integrated Pedersen and Hall conductivities. Note in particular that the KRMnumerical scheme [Kamide et al., 1981] accepts essentially any anisotropic distri-bution of the conductivities. In spherical coordinates θ [colatitude] and λ [eastlongitude], one obtains

A ∂ 2 Φ ∂ θ 2 + B

∂ Φ ∂ θ

+ C ∂ 2 Φ ∂ λ 2

+ D ∂ Φ ∂ λ

= F (14)

where the coefficients of this second-order differential equation are given by

A = sin θ ΣH, D = ∂ ΣP

∂ θ +

∂ Σ Hsin θ ∂ λ

,

B = ∂ sin ( θ ΣH )

∂ θ + ∂ ΣP

∂ λ ,

C = ΣH

sin θ , F =

∂ ∂ θ

sin θ ∂ ψ ∂ θ

+ 1

sin θ ∂2 ψ ∂ λ2

With a given current function ψ [or its function, F] and given conductivities andtheir gradients [in A, B, C, and D], the electric potential Φ can be solved for cer-tain boundary conditions. Once the electric potential is obtained by solving Eq.(14) numerically, the components of the height-integrated ionospheric current canbe readily calculated by Eq. (9). By inserting the ionospheric currents into Eq.(10), it is possible to derive the distribution of the field-aligned current density,obtaining the three-dimensional current system.

214

Figure 17. Average distribution of the ionospheric electric potential for the five phases ofsubstorms. The maximum and minimum potential values, as well as the total potential differ-ence are shown for each diagram. Contour interval: 5 kV. After Kamide et al. [1996].

Many recent studies have proven that the magnetogram-inversion technique is apowerful tool for evaluating quantitatively the three-dimensional current systemsresponsible for magnetic disturbances that occur at high latitudes associated withauroral displays. These “remote-sensing” schemes have also been shown to bequite useful in discussing magnetosphere-ionosphere coupling and in providingbasic information, such as the electrostatic potential at the polar cap boundary,numerical modeling of magnetospheric plasma processes [Wolf and Kamide,1983] and thermospheric wind patterns through the Joule heat dissipation fromthe ionospheric current. Unlike satellite measurements, the determination of elec-trodynamic parameters in the high-latitude ionosphere, using the magnetogram-inversion scheme, is not based on in situ data, but rather primarily on indirectmagnetic measurements on the earth’s surface. However, with the magnetogram-inversion scheme it is possible to estimate the ionospheric quantities on a globalscale [instead of only along satellite orbits] with a time resolution of about 5 minor even less over extended periods of time.

215

Figure 18. Average distribution of ionospheric current vectors for the five phases of sub-storms. The scale length of vector arrows is shown at the bottom. After Kamide et al. [1996].

The development of this particular method in the field benefited from consider-able progress in other areas, such as in situ or more direct observations of electricfields by satellites and incoherent scatter radars. It would be useful to modifythe numerical algorithm in such a way that simultaneous measurements of electricfields, conductivities, and field-aligned currents by satellite and radar could beincorporated into the scheme.

7.2. Applications to substormsThe KRM algorithm has been applied to a number of different sets of ground-based magnometer data for both quiet and disturbed periods. In this section wedemonstrate one such recent study in which the KRM algorithm was extensivelyused to obtain the average patterns of ionospheric parameters for the differentsubstorm phases. Five-minute resolution magnetometer data from the IMS merid-ian chains of observatories constitute the basic data set to estimate the distributionof ionospheric electric fields and currents as well as of field-aligned currents.From this data set, Kamide et al. [1996] have identified quiet times and four sub-storm phases: the growth phase, the expansion phase, the peak time, and the re-covery phase.

216

Figures 17 and 18 show the global distribution of the ionospheric electric poten-tial, and ionospheric current vectors, respectively, for the five different epochs. Toobtain these average patterns, each of the KRM output plots has been normalizedto the specific value: quiet time, –20 nT in the AL index, the growthphase, –100 nT; the expansion phase, –250 nT; the maximum epoch, –500 nT,and the recovery phase, –250 nT.

In Figure 17, the typical twin-vortex pattern in terms of the electrostatic poten-tial can be identified, except for the quiet time. It can be seen that the dynamicrange in the total potential difference is much smaller than that of the currentdensity, indicating that the electric field is relatively important during quiet times.The difference in the total potential drop across the polar cap between the growthphase and the expansion phases is only 2 kV. Similarly, the decrease in totalpotential from the peak to the recovery phase of substorms is only less than 10%,when the corresponding current decreases considerably from 500 nT to 250 nT.These results clearly demonstrate that a large-scale electric field is dominant notonly during the growth phase but also during the recovery phase of substorms.The overall pattern becomes most complicated during the recovery phase of sub-storms, as the relative size of the high/low potential vortices varies with respect tothe substorm phases. The location of the peak potential is different at differentsubstorm phases as well. With an increase in the electrojet current from thegrowth phase to the expansion phase, the peak of the high potential vortex ap-proaches the midnight sector while the peak location of the low potential vortexseems to remain at approximately 15:00-16:00 MLT.

Figure 18 shows the distribution of ionospheric current vectors correspondingto the five substorm phases. During the growth phase of substorms, the eastwardelectrojet expands both latitudinally and longitudinally, and its intensity is almostdoubled. The westward electrojet begins to grow during the growth phase and iscentered at 06:00 MLT. During the growth phase, the intensities of the eastwardand westward electrojets are nearly equal. At the expansion onset, however, themidnight portion of the westward electrojet is intensified dramatically, from lessthan 0.1 Am-1 before the expansion onset to nearly 0.4 Am-1 after the onset; how-ever, its morning portion remains almost the same. At the maximum epoch ofsubstorms, the westward electrojet extends over a wide MLT range including theevening sector where it intrudes into the region poleward from the eastward elec-trojet.

The substorm westward electrojet peaks in the midnight sector. It is signifi-cant that most of the changes in the current system occur as an addition of anintense westward current in the dark sector. During the recovery phase, the io-nospheric current pattern strongly parallels that of the growth phase.

217

SUN

ELECTRIC POTENTIAL

12

00 MLT

0618

expansionSubstorm

50°

Figure 19. Schematic diagram showing two pairs of the electric potential cells, representingthe effects of enhanced plasma convection and of the substorm expansion. The high potentialarea combining the two effects is hatched.

8. Future Direction

8.1. Two-component auroral electrojetInterest in electrodynamic phenomena in the earth’s high-latitude ionosphere

has recently increased to a significant degree. This is primarily because of theavailability of new experimental techniques for measuring a number of physicalquantities in the polar ionosphere, but also due to the growing realization that thehigh-latitude region play a key role in large-scale coupling between the magneto-sphere and the ionosphere.

How can the existence of the two electrojet components shown in Figure 14 beseen in the global potential patterns? Figure 19 is a schematic illustration of a pairof potential cells of enhanced convection and another pair of substorm expansioncells, coexisting during the expansion phase through the early recovery phase of asubstorm. The convection pair represents large-scale magnetospheric plasmaconvection, which is controlled primarily by solar wind-magnetosphere interac-tions, such as “merging” and “viscous-like” processes, whereas the substorm-expansion pair results from substorm activity centered in the midnight sector. It isthese substorm cells that are distorted strongly by enhanced ionospheric conduc-tivities and associated with intense auroral displays in the midnight sector.

Figures 17 and 18 show that the global patterns of electric fields and currents inthe ionosphere change systematically with the substorm phases. The changes can

218

be described in terms of two different components. Each one of the two compo-nents has its own characteristic distribution and timescale within the auroral elec-trojets. The auroral electrojet does not grow and decay as a whole; rather, only theportion in the midnight sector is enhanced at the time of auroral breakup. Theother portion is controlled primarily by the electric field, which does not neces-sarily reflect auroral activity. It is known that the substorm expansion develops ina longitudinally localized region near midnight and then expands both eastwardand westward, creating a conductivity-rich electrojet. The range of the conductiv-ity-rich electrojet is limited in local time, depending perhaps on the strength of thesubstorm expansion.

These two components can be identified as the signatures for the directlydriven and the unloading processes, respectively. The auroral electrojets associ-ated with direct energy input from the solar wind into the magnetosphere flowprimarily in the dusk and dawn sectors and increase in association with enhancedconvection. This is a typical signature for the substorm growth phase which pre-cedes the expansion phase onset.

Unloading of energy stored in the tail during the growth phase leads to the for-mation of the intense westward electrojet in the midnight sector during the expan-sion phase of a substorm. The enhancement in the conductivities results from anenhanced ionization caused by accelerated electrons, reflecting the unloading ofenergy from the magnetotail. It is important to emphasize that the directly drivencomponent is present throughout the entire lifetime of a substorm, indicating thatthe solar wind energy is continuously fed to the magnetosphere, though withvarying degrees. This component becomes, therefore, relatively dominant againduring the late recovery phase as the unloading component wanes. Because of theexistence of these two physically-different ingredients in the auroral electrojet, itis very important to locate a particular phenomenon observed by an incoherent-scatter radar with respect to the substorm-disturbed region. Caution must be exer-cised also to map accurtately the radar location to the auroral electrojet, which isquite dynamic during the expansive phase of substorms.

Some generally accepted interpretations have been found in a variety of obser-vations, leading to a first-approximation model for auroras and substorms andtheir associated current configuration, but there are many problems that are eithernot satisfactorily settled in terms of basic physical concepts or are still subject toconsiderable controversy. One of the difficulties lies in the fact that, like all othernatural phenomena, the magnetosphere-ionosphere system is influenced by manyunknown conditions and that it is impossible to repeat the same experiment in thesystem under constant conditions. Thus, one may often fail to find the crucialparameters that fundamentally control the whole system of the magnetosphere andthe polar ionosphere.

219

Many recent studies have dealt with the characteristic features of substormspresented by using a number of individual “snapshots” of the large-scale distribu-tion of high-latitude electric fields and currents at key substorms times. In par-ticular, a combination of ground-based and spacecraft data and modeling tech-niques, such as the AMIE technique [Richmond and Kamide, 1988] and the RCM[Rice Convection Model] algorithm, have been shown to be quite powerful inmapping the global patterns of the electric potential and their substorm changes. Itis also important to reveal that the thermospheric neutral winds accelerated byenergy dissipation processes associated with substorms do significantly influencethe ionospheric and magnetospheric electrodynamics [e.g., Forbes and Harel,1989; Lu et al., 1995].

During the long history of the study of polar magnetic disturbances, magneticfield vectors observed on the “two-dimensional” earth’s surface were the onlytools from which the representative “three-dimensional” current system could beinferred. It is only during the last two decades that several new powerful tech-niques, including radars, have become available for studying the three-dimensional current system and, as a result, our knowledge of the large-scalecurrent distribution in the ionosphere and magnetosphere as well as the drivingelectric field has evolved considerably. Polar-orbiting satellites establish thatfield-aligned currents that supply the major portions of the auroral electrojets are apermanent feature of the magnetosphere, but satellite data are not capable ofdetermining how they close in the ionosphere. Measurements of the ionosphericelectric field data from radars have revealed how convection electric fields at highlatitudes relate to the substorm auroral electrojets. Without the systematic data setfrom incoherent scatter radars, it would not have been possible to shed light on somany outstanding issues in substorm research, resulting in perhaps ionosphericcurrents being merely inferred from ground magnetic records. It is very importantto realize that once enhancements in the ionospheric currents are separated intothose in the electric field and in the conductivity, a number of important but un-solved questions regarding substorm dynamics can be discussed quantitatively.

8.2. Future directionIn order to compare properly, as well as most effectively, magnetosphere-

ionosphere-ground signatures for substorms and convection, it is necessary toidentify what a radar is measuring with respect to such a “natural” frame of refer-ence as the convection/substorm frame, not in man-made coordinate systems suchas latitude, MLT, etc. This is particularly the case when substorm-disturbed re-gions need to be mapped from radar altitudes to the ground. It is also important tonote that statistical potential patterns do not always exist in individual cases, andmoreover, substorms themselves do not “know” where magnetic midnight islocated, although substorm expansion onsets have been reported to occur mostlikely near midnight in a statistical sense [Craven and Frank, 1991]. The follow-

220

ing is a list of some of the research subjects which will rely strongly on the im-proved measurements of the auroral ionosphere by incoherent scatter radars in thefuture:[1] Longitudinal changes in ionospheric parameters: Substorms undergo many

local, small-scale changes in the structure of the electric field and current in thepolar ionosphere, particularly in the dark sector. Statistical potential patternsdo not always conform to individual cases. It is important to identify local sub-storm signatures near midnight on the basis of a data set from the combinedsatellite and radar measurements of electric fields and worldwide ground-basedmagnetometers, where it can be shown that enhancements in the “normal”electric fields [generated by solar wind-magnetosphere interactions] and thesubstorm expansion-related electric fields can coexist during substorms. To-ward this goal, it is desirable to observe not only the latitudinal profiles of io-nospheric electrodynamics but also longitudinal changes of the parameters,particularly near the region of the head of the traveling surge.

[2] Role of the ionospheric conductivity: The auroral ionosphere is not only apassive medium. The ionospheric electric field would be modified or changedcompletely by polarization charges deposited by ionospheric currents nearstrong gradients in the conductivity distribution. The modified electric fieldwill then be mapped to the magnetosphere, the efficiency of which is of courseregulated by the existence of the “parallel” electric field. No systematic studyhas so far been conducted to answer the question: What role does the polarionosphere play in the expansion onset of substorms? Significant contributionsfrom incoherent scatter radars with fine resolution measurements are thereforeexpected.

[3] Importance of neutral winds in substorms: One very important but unsettledquestion is why the convection electrojet near dawn and dusk is still dominantat the late recovery phase, at which interval the interplanetary magnetic field ismost often northward-directed. It is conceivable that the electric field causedby neutral winds in the thermosphere becomes relatively dominant during therecovery phase. In fact, according to Killeen et al. [1985], DE 2 observationsindicate that the thermosphere neutral wind is influenced by E- and F-regionion drifts with a few hours of time delay at high latitudes. The thermospheredoes follow convecting plasmas in the ionosphere with [unknown] time lags,generating thermospheric winds [Lyons et al., 1985]. It is this variation in theionosphere-thermosphere system that, in turn, alters electric fields and plasmaprocesses in the magnetosphere. Studies of this entire feedback system havenot even begun ins spite of its importance in understanding the magnetosphere-ionosphere-thermosphere coupling via electric fields, field-aligned currents,and particle precipitation. Further observations of the height dependence of theneutral wind by means of incoherent-scatter radars will offer a unique opportu-nity to examine the role of the neutral wind in the large-scale electric field atthe different phases of substorms.

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Acknowledgements:

I would like to thank Denis Alcaydé for his constant and consistent encouragement throught thepreparation of this manuscript. I also wish to thank Lou Frank for the use of his auroral imagedata.

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Brekke A., J. R. Doupnik, and P. M. Banks, Incoherent scatter measurementsof E region conductivities and currents in the auroral zone, J. Geophys. Res.,79, 3773, 1974.

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IONOSPHERE-THERMOSPHERE INTERACTIONS AT HIGHLATITUDES

A. D. Richmond

1. Thermosphere-Ionosphere EnvironmentThe thermosphere is that tenuous part of the Earth’s atmosphere lying between

about 85 km and 500 km. Its base is at the cold mesopause, where temperaturescan drop to 120 K. Its upper boundary with the overlying exosphere is indistinct,but is defined as that altitude where the mean free path of atoms and molecules isequal to the atmospheric scale height, that is, the distance over which pressuredecreases by a factor of 1/e. Below that altitude collisions between atoms andmolecules occur sufficiently frequently that the medium obeys the laws of fluidmechanics. The thermosphere’s name derives from the high temperature of itsupper portions, which measures at least 500 K but sometimes exceeds 2000 Kduring very disturbed conditions [Figure 1].

Figure 1. A typical atmospheric temperature profile and two extreme thermospheric tempe-rature profiles. Also shown are the altitudes of the tropopause, stratopause, mesopause, andthermopause which mark the upper limits of the troposphere, stratosphere, mesosphere, andthermosphere respectively, as defined by extrema in the temperature profile or, in the case ofthe thermopause (exobase), by the altitude where the atomic mean free path equals one pres-sure scale height. The ‘typical’ profile is also listed in Table 1. Note that the altitude scale islinear below 100~km and logarithmic above 100~km. (From Richmond, 1991).

The high temperature results from strong heating by solar ultraviolet radiationand, sporadically, by electric currents and energetic particle precipitation at highlatitudes. Cooling by infrared radiation is inefficient in the thermosphere, unlikelower atmospheric regions, so that the temperature tends to build up until down-

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ward heat conduction suffices to offset the heating. Thus the lower thermospherehas a strong vertical temperature gradient that helps to conduct the heat suffi-ciently rapidly.

The thermosphere is heterogeneous. Atomic oxygen, O, is produced by disso-ciation of molecular oxygen, O2, in the presence of solar ultraviolet radiation.Atomic oxygen can recombine by three-body collisions only in the lower thermo-sphere where collisions are frequent, and so its density in the upper thermospherebuilds up to the point that it becomes the dominant species above about 200 km.Long mean-free-paths in the upper thermosphere facilitate rapid diffusion, allow-ing the density of each species to decrease with increasing altitude according to ascale height that is determined by its individual mass, rather than according to anaverage scale height as is the case in the well-mixed lower atmosphere. Figure~2shows how the densities of heavier species like molecular nitrogen and oxygendecrease more rapidly with increasing height than the lighter atomic oxygen.

Figure 2. Typical number densities of major thermospheric neutral species, along with typicalday and night electron densities. The major constituents N2 and O2 are fully mixed below 100

km, while rapid diffusive separation occurs above 120 km. (From Roble, 1977).

Note that the exponential rate of density decrease is less in the upper thermo-sphere [above 150 km] than below, largely owing to the high temperature thatproduces a large scale height. Typically, the atomic-oxygen scale height is on theorder of 50 km in the upper thermosphere, as compared with a total-density scaleheight of only 5 km in the cold mesopause region.

The ionosphere is composed of the ions and free electrons embedded in theupper atmosphere, created by extreme-ultraviolet and X-ray radiation [togethersometimes called XUV radiation] and by energetic particles precipitating from themagnetosphere. The F region of the ionosphere, lying at altitudes of 150 km to1000 km, usually contains the largest electron- and ion-density concentrations.

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The peak electron density generally lies at altitudes of around 200-400 km atmiddle and high latitudes. Figure~2 shows typical midlatitude daytime andnighttime electron-density distributions. Even at the peak, the number density ofelectrons is only on the order of 10-3 that of the neutrals. To a very good approxi-mation the ionosphere is electrically neutral: there are equal numbers of electronsand singly charged positive ions at heights above 90 km. Minuscule departuresfrom electric neutrality, however, result in non-negligible electric fields. The ionsare influenced by a variety of photochemical, diffusive, dynamical, and electrody-namical processes that largely determine the distributions of the ion and electrondensities.

The neutral and ionized components of the upper atmosphere interact strongly.Ions are created from neutrals by photoionization and auroral-particle impact, andthe ions interact chemically with the neutrals. Ions and electrons react strongly toelectric fields, both in terms of bulk transport and in terms of electric-currentflow. Through collisions with the neutrals, the ions transfer momentum and exerta major influence on upper-atmospheric winds. The Joule heating produced bystrong auroral electric fields and currents can affect the temperature, circulation,and composition of both the neutral and plasma constituents in important ways.The plasma density distribution is additionally affected by neutral winds thatinduce plasma transport along geomagnetic-field lines. Winds also modify theelectric fields and currents through dynamo action. The mutual interactionsamong neutral dynamics, plasma dynamics, and electrodynamics create a varietyof interesting phenomena that pose challenges for modeling and interpretation.

2. Gas Laws and Pressure CoordinatesThe partial pressure pj of the jth constituent of the upper atmosphere obeys the

ideal gas equation:

pj = nj k Tj, (1)

where nj is the number density of the constituent, k is the Boltzmann constant[1.381 10-23 J.K-1], and Tj is the temperature of the constituent. The temperatureis assumed here to be isotropic. The neutral constituents normally have equaltemperatures, but the electrons and ions can have higher temperatures than theneutrals. The total number density n and total mass density ρ are:

n = ∑j

nj (2)

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1 2 3 4 5 6 7 8 9 10 11 12z Τ m Η ρ ne DE/H2 µm/ρH2 σPB2/ρ σHB2/ρ 2π/N C

(km) (K) (amu) (km) (kg.m-3) (m-3) (10-4s-1) (s) (m.s-1)0 288 29.0 8.4 1.23+00 594 178

10 223 29.0 6.6 4.14-01 525 15720 217 29.0 6.4 8.89-02 293 27330 227 29.0 6.7 1.84-02 293 28740 250 29.0 7.4 4.00-03 287 32550 271 29.0 8.0 1.03-03 339 29860 247 29.0 7.4 3.10-04 .005 384 24170 220 29.0 6.6 8.28-05 4.04+08 .012 364 22780 199 29.0 6.0 1.85-05 9.85+08 .033 .000 329 22890 189 28.9 5.7 3.12-06 2.11+10 .037 .001 .000 307 234

100 191 28.4 5.9 5.30-07 1.39+11 .032 .008 .000 .016 260 285110 236 27.3 7.6 8.92-08 1.49+11 .006 .033 .015 .097 230 416120 372 26.1 12.5 1.91-08 1.54+11 .000 .077 .231 .295 246 640130 507 25.2 17.8 6.95-09 1.56+11 .131 .489 .217 308 724140 613 24.5 22.2 3.38-09 1.58+11 .197 .551 .116 361 771160 763 23.3 29.2 1.19-09 1.67+11 .376 .598 .044 447 820180 856 22.2 34.5 5.39-10 1.84+11 .640 .722 .027 513 846200 914 21.2 38.8 2.80-10 2.98+11 1.02 1.27 .027 564 866250 981 19.2 46.8 7.40-11 1.10+12 2.79 5.52 .037 652 902300 1002 17.8 52.4 2.45-11 1.32+12 6.81 7.54 .019 710 928350 1009 16.8 56.7 9.21-12 1.16+12 15.6 7.01 .007 755 943400 1011 16.1 60.2 3.74-12 8.21+11 34.0 5.15 .002 786 963500 1012 14.6 68.2 7.10-13 3.23+11 140. 1.97 .000 814 1054600 1012 12.2 84.5 1.55-13 1.46+11800 1012 6.0 182. 1.42-14 6.65+10

1000 1012 4.0 289. 4.07-15 5.38+10

Table 1: Typical daytime upper atmospheric parameters. Columns~2-5 are from the U.S.Standard Atmosphere (1976) at altitudes of 80 km and below, and from the MSIS-86 ther-mospheric model (Hedin, 1987) at 90 km and above (for March equinox, 30° north latitude,

11 local time, solar 10.7 cm flux = 120 10-22 W.m-2.Hz-1, Ap magnetic activity index = 10).

Electron densities (column 6) are from the International Reference Ionosphere (for Marchequinox, 30° north, 200° east, 11 local time, sunspot number = 70). Eddy diffusion coeffi-cients are from the U.S. Standard Atmosphere (1976) at 90 km and above, and are assumed to

decrease at lower heights. A number like 4.04+08 means 4.04 108. The characteristic rates incolumns 7-10, as discussed in Section 5, are given as multiples of the characteristic rate for

coriolis effects, 10-4 s-1.Adapted from Richmond (1991).

Z: altitude;T: temperature;m: mean molecular mass(1 amu=1.661 10-27 kg);H: pressure scale height;ρ: mass density;ne: electron number density;

DE : the eddy diffusion coefficient;

µm: the molecular viscosity coefficient;

σP,σH: Pedersen and Hall conductivities;

B: geomagnetic field strength;N: the angular Brunt-Väisälä frequency;C: the limiting speed for simple gravity waves.

231

ρ = ∑j

nj mj (3)

where mj is the mass of the j constituent.

The mean molecular mass is:

m = ρ n (4)

The relation of the total pressure p to the density is obtained by summing Eq. 1over all species:

p = ∑j

nj k Tj =

ρ m k T , (5)

where the mean temperature is defined as

T = p

n k (6)

Since the neutrals dominate the total gas density, T is essentially the neutraltemperature. The internal energy density of the gas per unit mass is cv T, and thespecific enthalpy is cp T, where cv and cp are the specific heats at constant volumeand pressure, respectively, which are related by:

cp = cv + k m (7)

For a pure monatomic gas like O, cv would be 3/2 ( k / m ), while for a purediatomic gas like N2 or O2, cv would be 5/2 ( k / m ). Typical values of the totaldensity, temperature, and mean molecular mass are listed in Table 1.

Under most circumstances the atmosphere is in "hydrostatic equilibrium",meaning that the vertical pressure gradient force balances gravity:

∂ p ∂ z

= - ρ g = - p H (8)

H = k T m g (9)

232

where z is altitude, g is the acceleration of gravity, and H is the "pressure scaleheight", the exponential scale by which pressure decreases with increasing alti-tude.

When hydrostatic equilibrium holds, pressure or its negative logarithm

Z = - ln

p p0 (10)

where p0 is an arbitrary reference pressure, can be used as a vertical coordinate inplace of z.

Two advantages of using "pressure coordinates are that upper-atmosphericphenomena tend to be better organized with regard to pressure than altitude, andthat the equations of large-scale dynamics assume a simpler form when Z ratherthan z is the independent variable.

The dependent variable that replaces p is the "geopotential" Φ:

Φ ( z ) = ⌡⌠

0

z g ( z’) d z’ (11)

which varies approximately linearly with altitude, except for variations associatedwith the relatively small decrease of g with increasing height.

The hydrostatic equation 8 becomes:

∂ Φ ∂ Z

= g H (12)

A dimensionless vertical velocity W can be defined as:

W = - 1 p

d p d t (13)

where the derivative of p with respect to time t is taken following the motion ofthe fluid element.

When multiplied by H, W represents the vertical velocity relative to a constant-pressure surface, which itself may be moving with respect to the Earth.

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3. Mass ContinuityEach constituent satisfies a continuity equation:

mj ∂ nj

∂ t + . ( mj mj vj ) = Pj (14)

where vj is the mean velocity of the particles and Pj is the net photochemicalproduction rate, i.e., the difference between production and loss. If the meanvelocity of the medium is defined as:

v = 1 ρ

∑j

mj nj vj (15)

then the velocity vj of the constituent can be expressed as:

vj = v + vdj (16)

where vdj is the "diffusion velocity", i.e., the velocity of the j species with respectto the mean velocity of the medium.

The mean velocity v is essentially the neutral wind velocity, since neutrals byfar outnumber ions. The total-gas continuity equation is obtained by summingEq. 14 over all species. In this process, the diffusion fluxes sum to zero and thenet production terms cancel because of mass conservation:

∂ρ ∂t

+ . ( ρ v ) = 0 (17)

Under hydrostatic equilibrium, the mass contained between two constant-pressure surfaces is essentially constant, since the pressure difference between thetwo surfaces is equal to the weight per unit area of the air between them. Thetotal-gas continuity equation can then be written as:

1 p

∂ ∂ Z

( p W ) + p . vh = 0 (18)

where vh is the horizontal wind component and where the subscript p on ∇ p

indicates that the horizontal partial derivatives associated with the ∇ operator aretaken with p [or Z] held constant rather than z.

In the thermosphere, photochemical production and loss are relatively unim-portant processes for molecular nitrogen and for the minor species argon, helium,

234

and atomic hydrogen. On the other hand, photochemical processes are importantfor the major thermospheric constituent O and for minor constituents like N andNO. Thermospheric atomic oxygen is created by photodissociation of molecularoxygen. It is lost by recombination into diatomic oxygen in three-body collisionsthat require a relatively dense atmosphere. Thus loss of O occurs primarily nearthe base of the thermosphere. The production and loss rates of O2 are basicallyjust one-half the O loss and production rates, respectively, since mass must beconserved. At 200 km, roughly 4 % of the O2 molecules are photodissociatedduring 12 hours of sunlight. At 100 km, roughly 1 % of the O atoms recombine toO2 during a 24-hour day. Because these fractions are relatively small, photo-chemical production and loss of O and O2 can be ignored when dynamicalchanges happening in less than a day are being considered.

In contrast, the lifetimes of ions are relatively short. When sunlight or strongauroral particle precipitation is present, the lifetimes of the dominant ions be-tween 90 km and 150 km are on the order of one minute; production and loss areoften nearly in balance, and "photochemical equilibrium" prevails. At higheraltitudes the loss rate slows down because of a change in composition from pre-dominantly molecular ions, which recombine rapidly with electrons, to atomic

Figure 3. (Left) Typical ion production rates from various sources. Solid lines show regularsources. During the day, direct solar extreme ultraviolet (EUV) light is the main ionizationsource. At night, EUV scattered from the geocorona as well as that from stars helps maintainthe E-region ionosphere. Other sources are highly variable in time, and are shown withdashed lines: solar-flare X rays and EUV (dayside only) and auroral electrons and solarcosmic rays (high latitudes only). (Middle) Representative time scales at various altitudes fordifferent physical processes affecting the daytime ionosphere. (Right) Typical daytime ion andelectron densities. (From Richmond, 1987).

235

oxygen ions, which are lost primarily by charge-exchange reactions with therelatively sparse diatomic nitrogen and oxygen molecules. Transport by meanmotions as well as by diffusion parallel and perpendicular to the geomagneticfield then has time to have a significant impact on the plasma densities.

Figure 3 illustrates the height distributions of various ion production rates anddaytime ion densities, along with characteristic time scales of chemical loss, ofdiffusion, and of advection.

The ionosphere is horizontally stratified on the large scale, meaning that verti-cal gradients of densities are normally much stronger than horizontal gradients.Consequently, the vertical component of ion transport by advection [ v ] and bydiffusion [ vdj ] usually has a greater impact on ion density than does the hori-zontal component of transport. [Exceptions to this can occur in the polar regionwhere rapid horizontal ion drift velocities convect plasma over significant dis-tances, creating "tongues" and "troughs" of plasma density]. In the F-regionelectric fields convect plasma perpendicular to the magnetic field at the velocity:

ue = E x B

B2 (19)

where E and B are the electric and magnetic field vectors.

For a strong auroral electric field of 0.1 V.m-1 and a typical magnetic-fieldstrength of 5. 10-5 T, the magnitude of ue is 2000 m.s-1. Where B is tilted awayfrom the vertical this drift can have a vertical component: a typical drift magni-tude of 300 m.s-1 in the magnetic meridional plane has about a 50 m.s-1 verticalcomponent when B has a dip angle I = 80°, i.e., when it is 10° off-vertical. Overthe roughly 1-hour lifetime of F-region ions, that vertical drift alone would movethe ionosphere about 200 km if other effects like diffusion along geomagnetic-field lines did not also intervene.

Neutral winds at F-region heights tend to impose their velocity componentprojected along B onto the ions, although again diffusion can intervene to modifythe net ion velocity along B. The large-scale winds are predominantly horizontal.A wind v in the magnetic northward direction has a projection of v cos I along themagnetic field line B, which in turn projects along the upward direction with avalue - v cos I sin I. A typical value of 120 m.s-1 for v in the magnetic meridionalplane thus tends to impose a vertical motion on the order of 20 m.s-1 on theplasma for I = 80°, downward if the wind is poleward, and upward if the wind isequatorward. The neutral-wind effect generally increases in importance withdecreasing magnetic latitude in the polar regions because of the factor cos I. Atlow magnetic latitudes the factor sin I intervenes to make the neutral-wind effecton plasma motions again small.

236

Figure 4. Molecular- and eddy-diffusion coefficients.(From U.S. Standard Atmosphere, 1976).

4. Diffusion Velocities and Electric CurrentsFor neutral species, the diffusion velocity can be calculated from:

vdj = Dj

- nj nj

- ( 1 + αj ) T T +

mj k T g - DE ln

mj nj

ρ (20)

where Dj is the molecular diffusion coefficient, αj is the thermal diffusion coeffi-cient, and DE the eddy diffusion coefficient.

Thermal diffusion turns out to be important primarily for the light species Hand He, for which the U.S. Standard Atmosphere [1976] uses values of αj = 0.40.Figure 4 shows estimated mean values of the diffusion coefficients in the heightrange 85-150 km.

Molecular diffusion is dominant above 110 km, while eddy diffusion dominatesbelow 100 km. The crossover point, which can vary in space and time, is oftencalled the "turbopause".

In the upper thermosphere Dj is very large, and in order for moderate diffusionvelocities to be maintained the multiplier of Dj in Eq. 20 must be small. In thissituation, called "diffusive equilibrium", nj varies with height z as:

237

nj = nj0

T0

T

1+α j

exp

- ⌡⌠

z0

z

d z’ Hj (z’) (21)

Hj ≡ k T mj g (22)

where nj0 and T0 are the number density and temperature at the arbitrary referenceheight z0 and Hj is the pressure scale height of the jth species.

The rate of exponential density decrease with altitude thus depends on the massof the species, and lighter species decrease less rapidly in density with increasingaltitude than heavier species, as apparent in Figure 2.

For charged species, the Lorentz force associated with electric and magneticfields comes into play. Thermal diffusion is usually ignored. It is convenient toconsider separately diffusion parallel and perpendicular to the geomagnetic fieldB. Parallel to B the diffusion velocity of the jth species is:

vdj// = 1 νj

- 1

nj mj ∂ pj

∂ s + g . b +

qj mj

E// (23)

where νJ is the effective "collision frequency" for momentum transfer with otherspecies, s is distance along B, b is a unit vector along B, qj is the particle charge,and E// is the electric-field component parallel to B.

The ion collision frequency is dominated by collisions with neutrals, and de-creases exponentially with increasing altitude. The electron collision frequency isdominated by collisions with neutrals below about 200 km, but at higher altitudescollisions with ions can dominate.

For electrons, the terms in parentheses in Eq. 23 are usually in approximatebalance above 150 km, where νJ is relatively small; if they were not, very largeelectron diffusion velocities would result. The small mass of electrons causes thegravitational term in Eq. 23 to be negligible in comparison with the pressure-gradient and electric-field terms. Under these conditions,

E// ≈ - 1

ne qe ∂ pe

∂ s , (24)

238

where subscripts e refer to electrons, and where qe is the magnitude of theelectron charge [1.602 10-19 C].

This parallel electric field has a downward component below the F-region peak,and an upward component in the topside ionosphere. Its magnitude is on the orderof 10-6 V.m-1, estimated from the quantity k Te / qe L, where Te is the electron

temperature [∼ 103 K] and L is a characteristic scale length for electron-densitygradients [∼ 105 m].

Consider for simplicity that there is a single positive ion species [e.g., O+].When Eq. 24 is used in Eq. 23 for the ions, the latter equation becomes:

vdi// = 1 νi

- 1

ni mi ∂ (pi + pe)

∂ s + g . b (25)

where subscript i refers to ions.

The ion and electron partial pressures are comparable, being in the ratio of theion and electron temperatures. Thus the effective pressure that contributes to iondiffusion is considerably greater than the ion pressure alone. The strong electriccoupling between ions and electrons tends to cause them to tend to diffuse to-gether, a process called "ambipolar diffusion". In the high ionosphere, where 1/νi

is very large, the two terms in brackets in Eq. 25 must nearly balance, producing astate of "diffusive equilibrium". In this situation, the plasma scale height is deter-mined essentially by the ion mass and the sum of the ion and electron tempera-tures, and it is thus greater than the scale height of neutral atoms that have a massand temperature equal to those of the ions.

A small deviation of E// from the value that balances the ion and electron ve-locities parallel to B, i.e. from the value approximately given by Eq. 24, will resultin different ion and electron velocities, and therefore an electric current. Let usdenote the deviation by E’// . It is primarily the electron velocity that is affected,since electrons are much more mobile than the massive ions. The parallel currentdensity is approximately:

J// = ∑j

nj qj vdj// = σ// E’// ≈ ne qe vde// ≈

ne qe2

me νe E’// (26)

where σ// is the "parallel conductivity".

Typical daytime values of σ// are shown in Figure 5.

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Figure 5. Noontime parallel (σ//), Pedersen (σP), and Hall (σH) conductivities at 44.6°N,

2.2°E, for solar-minimum conditions on March 21. (From Richmond, 1995b).

In the upper ionosphere they are on the order of 102. Normally, J// is on theorder of 10-5 A.m-2 or less, even in regions of strong auroral currents. Thus, E’// isusually less than 10-7 V.m-1 in the upper ionosphere, much less than the fieldassociated with ambipolar diffusion.

Perpendicular to the geomagnetic field, the dominant forces on charged parti-cles are the Lorentz force and the frictional force due to collisions with neutrals.Neglecting the gravitational and pressure-gradient forces, the force-balancecondition is:

qj [ E⊥ + ( v + vdj⊥ ) . B ] - mj νj vdj⊥ = 0 (27)

where subscripts ⊥ denote the component perpendicular to B.

Equation 27 can be solved for vdj⊥ by vector algebra:

vdj⊥ = νj Ωj ( E⊥ + v x B ) - Ωj2 b x ( E⊥ + v x B )

B ( νj2 + Ωj2) (28)

where Ωj is the [signed] angular "gyrofrequency" of the jth species,

240

Ωj = qj B mj

(29)

It is the electric field measured in the reference frame moving at velocity v,[ E⊥ + v x B ], that drives the perpendicular diffusion. The electric current per-

pendicular to B is:

J⊥ = ∑j

nj qj vdj⊥ = σP ( E⊥ + v x B ) + σH b x (E⊥ + v x B ) (30)

where the "Pedersen σP" and "Hall σH " conductivities are:

σP = ne qe

B

νe Ωe

νe2 + Ωe2 + νi Ωi

νi2 + Ωi2 (31)

σH = ne qe

B

Ωe2

νe2 + Ωe2 - Ωi2

νi2 + Ωi2 (32)

Equations 31 and 32 are derived under the approximation that the collisionfrequencies and gyrofrequencies of all ion species are represented by the meanvalues νi and Ωi, respectively. Typical values of σP and σH in the sunlit iono-sphere are shown in Figure 5.

Equations 26 and 30 are an expression of Ohm’s Law, with the current densityproportional to the effective electric field; however, the factors of proportionalityrepresent a tensor rather than a scalar. That is, the current does not flow in thedirection of the electric field. Because the parallel conductivity is so large, E’//

must normally be very small in order for the electric current to remain moderate.Thus the electric field tends to be nearly perpendicular to the geomagnetic field,even though current readily flows both along and across the field. In the planeperpendicular to the geomagnetic field, the direction of the current can make anangle of up to 88° with respect to the electric field, which occurs at around 100km altitude.

5. Neutral DynamicsUnlike charged-particle motions, horizontal neutral motions are not in force

balance, and inertia must be taken into account. If all the neutrals are treated as asingle fluid, as is usually appropriate except when diffusive effects need to beconsidered, the following momentum equation applies:

241

d v d t + 2 x v +

p ρ

+ ∇ . S

ρ = g +

J x B ρ

(33)

where is the angular rotation rate of the Earth, of magnitude 7.29 10-5 s-1, andS is the viscous momentum flux tensor or viscous stress tensor.

This equation is expressed in the rotating reference frame of the Earth, whichresults in the appearance of the "Coriolis acceleration" - 2 x v [see e.g. Holton,1979]. The centrifugal acceleration associated with rotation has been absorbedinto the total gravitational acceleration g in Eq. 33. The term (J x B) / ρ is the"Ampère acceleration".

It is conceptually useful to write the Ampère acceleration in terms of the differ-ence between the neutral velocity and the electrodynamic velocity ue defined byEq. 19. By making use of Ohm's Law Eq. 30, we can obtain:

J x B ρ

= σP B2

ρ (ue - v⊥ ) +

σH B2

ρ b x (ue - v⊥ ) (34)

where v⊥ is the component of v perpendicular to B, and where the quantities

σP B2 / ρ and σH B2 / ρ are sometimes called the "Pedersen-drag" and "Hall-drag" coefficients.

The first term in Eq. 34 causes acceleration of the air, perpendicular to themagnetic field, in the direction of the electromagnetic drift and opposite to thedirection of the wind. It tends to accelerate the wind towards the electrodynamicvelocity. At altitudes where the ion angular gyrofrequency exceeds the ion-neutralcollision frequency and where ions drift at nearly the electrodynamic velocity ue

[above about 130 km], the Pedersen-drag coefficient σP B2 / ρ is just the meanrate at which a neutral particle suffers a collision with an ion. This rate is propor-tional to the ion [and electron] density, which varies considerably with altitude,time of day, latitude, season and solar cycle. It is also often called the "ion-drag"coefficient. The second term in Eq. 34, proportional to σH B2 / ρ, acts at a rightangle to the first. When v⊥ is more important than ue this component of accelera-tion tends to turn the wind in a manner similar to the Coriolis effect. Because thegeomagnetic field is downward over most of the northern hemisphere and upwardover most of the southern hemisphere, the horizontal component of this deflectingacceleration is opposite to the Coriolis acceleration.

The horizontal momentum equation, under the assumption that viscous stressesare predominately associated with vertical shears of horizontal winds, can bewritten:

242

d vh

d t + f z x vh + p Φ - 1

ρ H

∂ ∂ Z

µm + µturb

H ∂ vh

∂ Z

+ σP B2

ρ ( ve + sin2 I vn ) -

σH B2

ρ sin I z x vh

=σP B2

ρ ( uee + sin2 I uen ) -

σH B2

ρ sin I z x ueh

(35)

f = 2 Ω sin λ (36)

where λ is geographic latitude; z is a unit upward vector; µm and µturb are themolecular and turbulent coefficients of viscosity; subscripts e and n denotecomponents in the magnetic eastward and northward directions, respectively; andh denotes a horizontal component.

The horizontal pressure-gradient acceleration is represented by p Φ in pres-sure coordinates. The coefficient of molecular viscosity is approximately:

µm = 1.87 10-5

T

273.15 0.69

kg.m-1.s-1 (37)

while the coefficient of turbulent viscosity is commonly related to the turbulentdiffusion coefficient by:

µturb = ρ DE Pr (38)

where Pr is the "Prandtl number", whose value depends on the nature of theturbulence, but is generally greater than unity.

The relative importance of the terms in Eq. 35 for horizontal motions is vari-able. When certain terms are relatively small, their effects can often be neglected.A useful way to determine the most important terms is to evaluate characteristictime rates associated with each, where the appropriate rate for a term is a typicalmagnitude of that term divided by a typical value of the wind velocity. Thoseterms having the largest rates are most important. A diurnal variation of the wind,with an angular frequency of 2 π / (1 day), has a characteristic rate equal to thatfrequency, or 0.7 10-4 s-1. More rapid wind variations like those associated withgravity waves have correspondingly greater rates. The horizontal component ofthe Coriolis acceleration has a characteristic rate of f, which varies with latitudebut is on the order of 10-4 s-1 at midlatitudes.

To estimate a characteristic rate for molecular viscosity, we can use the pres-sure scale height H as a typical vertical scale length for large-scale motions, andreplace derivatives with respect to altitude by 1/H, obtaining a characteristic time

243

rate of µm / ρ€ H2. That quantity is listed in Table 1. It increases rapidly withaltitude, and is comparable with the inertial rates around 200 km. Because viscos-ity must be balanced by the other terms in Eq. 35, its characteristic rate cannotincrease indefinitely with altitude, but tends to saturate by virtue of the fact thatthe vertical shear of the wind decreases, so that the characteristic vertical scalebecomes greater than H. On the other hand, the vertical scale can be less than Hfor some types of motions, like gravity waves with short vertical wavelengths, andthese motions may be strongly influenced by viscosity well below 200 km.

The characteristic rate for turbulent viscosity is DE Pr / H2. The values ofDE / H2 listed in Table 1 give a lower estimate for this rate [i.e., with Pr = 1].

The Pedersen-drag term on the left-hand side of Eq. 35 has a characteristic rateof σP B2 sin2 I / ρ in the magnetic north-south direction and σP B2 / ρ in themagnetic east-west direction. The Hall-drag term has a characteristic rate ofσH B2 sin2 I / ρ. Typical daytime values of the Pedersen-drag and Hall-dragcoefficients are listed in Table 1. The daytime Hall-drag rate can become compa-rable to the inertial rates around 125 km, but it falls off above that altitude. Thedaytime Pedersen-drag rate increases steadily with altitude up to the peak of the Fregion, where it can easily exceed 10-3 s-1.

Figure 6. (Left) Horizontal component of parameterized electrodynamic drift velocities ue

(arrows) and energy flux of precipitating electrons (contours with intervals of 0.75 mW.m-2 at12:30 UT on 22 March 1979. (Right) Simulated neutral winds (arrows) and temperatures(contours labeled in kelvins) at approximately 300 km, at 12:30 UT on 22 March 1979. (FromRoble et al., 1987).

244

At midlatitudes, the electrodynamic velocity ue is often considerably smallerthan the wind velocity v, and the main effects of the Ampère acceleration are justthose of the Pedersen- and Hall-drag terms on the left-hand side of Eq. 35. Athigh magnetic latitudes, ue often exceeds v in magnitude, so that the terms on theright-hand side of Eq. 35 can dominate, acting as forcing terms that accelerate thewind rapidly towards the ion convection velocity.

There is no simple characteristic rate associated with the horizontal pressuregradient. For long time scales the pressure sometimes tends to adjust throughdensity and temperature changes of the air in such a way as to come into balancewith the other forces. For example, in the lower thermosphere where ion drag andviscosity are often unimportant, it is possible to have part of the air motion ingeostrophic balance, with the horizontal pressure-gradient force approximatelybalancing the Coriolis force. Such a situation is common in the lower atmosphere,where winds tend to flow along isobars. In the upper thermosphere, the pressure-gradient force will tend to be in approximate balance with the ion-drag andviscous forces. When ue is small, all three forces in the upper thermosphere tendto be parallel to the wind direction: the wind is directed more nearly perpendicularto isobars than parallel to them. Since the upper-thermospheric pressure is largeron the day side than on the night side of the Earth, owing to daytime thermos-pheric expansion, the wind blows generally away from the day side toward thenightside in the upper thermosphere.

Figure 6 shows the distributions of ion and neutral velocities at 300 km be-tween 47.5° geographic latitude and the North Pole, as simulated by the NationalCenter for Atmospheric Research Thermosphere General Circulation Model[NCAR TGCM]. The simulation is for a geomagnetic storm. The imprint of thepattern of ion convection on the neutral velocity in the auroral zone and polar capis evident. Ion drag tends to accelerate the neutrals towards the ion velocity, butinertia and competing forces prevent full coincidence between the ion and neutralvelocities. The imprint of the evening cell of the polar ion-convection patternappears clearly in the neutral velocity, but the imprint of the morning cell is lesspronounced, in part because of lower electron density, and hence ion-drag, duringthe latter part of the night.

6. Energy Balance, Temperatures, and Vertical WindsThe temperature and pressure variations in the thermosphere respond to ex-

changes of energy. The equation for conservation of thermodynamic energy canbe expressed in terms of the rate of change of pressure and of specific enthalpy as:

245

d d t ( cp T ) -

1 ρ

d p d t +

1 ρ

. q = Q (39)

where q is heat flux and Q is the net heating associated with a variety of proc-esses: absorption of solar ultraviolet radiation, heat deposition by energeticmagnetospheric particles, chemical heating, infrared cooling, viscous heating, andJoule heating.

In terms of high-latitude thermosphere-ionosphere interactions, Joule heating isof particular importance. The heating rate per unit mass is given by:

Figure 7. Decay of a temperature perturbation T by molecular heat conduction in an idea-lized atmosphere, with no other addition or loss of heat. T1 is the asymptotic high-altitude

temperature perturbation at t=0. Z is normalized altitude, measured in scale heights, and Z0

is the normalized transition altitude of the perturbation profile at t=0. τ0 is a time constant

equal to the inverse heat-conduction rate coefficient at Z0. See text for further explanation.

QJ = J . ( E + v x B)

ρ =

σP B2

ρ ( ue - v⊥ )2 (40)

The contribution of Joule heating to the heat budget of the thermosphere above130 km can exceed that of sunlight during aurorally disturbed periods. Duringdisturbed periods the height-integrated and globally averaged Joule heatingusually exceeds that associated with precipitating energetic particles by a factor of

246

2-3. Joule heating tends to occur higher than particle heating, where it has arelatively stronger effect on the thermospheric temperature because of the lowermass density.

The heat flux is due to molecular heat conduction, transport of heat in associa-tion with species diffusion, and turbulent heat conduction. On large scales, thehorizontal components of heat conduction can be neglected. The upward heat fluxis:

qz = - κm ∂ T

∂ z + ∑

j

( nj mj cpj+αj nj k T) z . vdj - κturb

g

cp +

∂ T∂ z

(41)

The molecular heat conduction coefficient κm is closely related to the molecu-lar coefficient of viscosity and is adequately approximated throughout the thermo-sphere by:

κm = 1.5 cp µm (42)

The turbulent heat conduction coefficient κturb is approximately related to theeddy diffusion coefficient by:

κturb = ρ DE cp (43)

The molecular heat conduction coefficient κm is closely related to the molecu-lar coefficient of viscosity and is adequately approximated throughout the thermo-sphere by:

κm = 1.5 cp µm (42)

The turbulent heat conduction coefficient κturb is approximately related to theeddy diffusion coefficient by:

In pressure coordinates, considering only the vertical component of heat flux,Eq. 39 becomes:

d

d t ( cp T ) + W g H

- 1

ρ H ∂

∂ Z

κm

H ∂ T ∂ Z

+ κturb cp H

g H + ∂

∂ Z ( cp T )

= Q

(44)

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Molecular heat conduction has a major effect on thermospheric energetics. Athigh altitudes rapid conduction is responsible for the nearly isothermal verticaltemperature profile. As with viscosity, a characteristic time rate for heat conduc-tion to be effective can be defined by considering the case where vertical gradi-ents have a characteristic scale of H. The characteristic time-rate-of-changeassociated with molecular heat conduction in Eq. 44 is then seen to be:

ακ = κm

cp ρ H2 (45)

Because of Eq. 42, the characteristic rate for molecular heat conduction is sim-ply 1.5 times that for molecular viscosity.

In order to understand the manner in which heat conduction affects the evolu-tion of the thermospheric temperature in response to a perturbation, it is instruc-tive to look at a simplified solution to a one-dimensional [vertical] version ofEq. 44, conceptually representative of a global average. Advection and turbulentconduction are ignored, and cp and κm / H are assumed constant. Eq. 44 thenyields

∂ T ∂ t

- ακ ∂2 T ∂ Z2

= Q ’ cp

(46)

where Q ’ is the perturbation heat input.

The characteristic rate ακ for heat conduction is assumed to vary with Z as

ακ ( Z ) = α0 eZ (47)

because of its inverse dependence on air density, where α0 is a constant.

Assume an initial temperature of the form:

T = T0 + T ’ = T0 + T1 exp - e ( Z0 - Z ) (48)

where T0, T1 and Z0 are constants.

The initial profile of T ’ / T1 [ at t = 0 ] is plotted in Figure 7. T becomes as-ymptotically isothermal at low and high altitudes, where it approaches values ofT0 and T0 + T1, respectively. Z0 represents a normalized transition altitude be-tween these two asymptotic regimes. The solution to Eq. 46, assuming that Q ’ = 0after t = 0, is:

248

Figure 8. Meridional wind and streamlines between 80 km and 450 km averaged over 12hours of a simulated storm at solstice using a two-dimensional model. The Z level is definedby a value of p0 = 1.05 Pa in (10). The wind-barb notation is as follows: short barb (5 m.s-1);

long barb (10 m.s-1); and flag (50 m.s-1). The vertical components of the winds have beenscaled so that the shafts of the wind arrows are parallel to streamlines. The normal summer-to winter flow is altered by Joule heating that is centered around 21° and 159° colatitude. Thesummertime equatorward flow is strengthened, while the normal wintertime poleward flow isreversed at middle latitudes. (From Brinkman et al., 1992).

T ’( Z , t ) = T1 τ0

t + τ0 exp

- τ0 e ( Z0 - Z )

t + τ0 (49)

τ0 = 1

ακ (Z0) (50)

This solution retains the same functional form as the initial temperature pertur-bation profile, but the maximum perturbation decreases as 1 / ( t + τ0 ) and the

normalized transition altitude lowers as - ln ( 1 + t / τ0 ) with increasing time, as

seen in Figure 7. The characteristic rate for molecular heat conduction, ακ ,determines how rapidly the perturbation penetrates to lower heights, and howrapidly it decays in time.

The conductive response to variations in heating can dominate globally aver-aged temperature variations. Spatially localized heating, however, tends to pro-

249

duce advective motions that can dominate the local response. In particular, local-ized heating makes the air more buoyant that its surroundings, causing it to rise.The adiabatic cooling associated with the vertical advection tends to come intorough balance with the heating after some period of time, at least at lower alti-tudes where heat conduction is not too rapid. This cooling is represented by thefirst two terms on the left-hand side of Eq. 44 when the time derivative followingfluid motion, d ( cp T ) / d t, is dominated by the vertical advective derivative

W ∂ ( cp T ) / d Z. Balancing these two terms with the heating then gives:

W ∂ ( cp T )

∂ Z + W g H ≈ Q (51)

This yields a [dimensional] vertical velocity of:

W H ≈ Q

g +[ ∂ ( cp T ) / ∂ Z ] (52)

An intense heating rate of 1000 W.kg-1, as would occur when the ion drag pa-rameter is 10-3 s-1 and the velocity difference between the neutrals and ions is1000 m.s-1, produces an upward velocity of the order 100 m.s-1 according to thisestimator. The upward motion in the region of net heating must be balanced byoutward flow at high altitudes and downward motion outside the heating region.This downward motion produces compressive heating, and thus the originallocalized heat input tends to become distributed over a larger area. Figure 8 showsan example of the mean meridional circulation driven by a combination of solarand auroral heating for storm conditions. The summer-to-winter flow is driven bysolar heating. Strong auroral Joule heating reverses that flow at upper midlati-tudes in the winter hemisphere.

The vertical circulation associated with non-uniform thermospheric heatingaffects the composition: air rich in heavier molecular species is raised to higheraltitudes in regions of net heating, while sinking motions elsewhere tend todeplete those species.

In addition, there can be horizontal transport of the altered air when the windsare strong, as illustrated in Figure 9. The high-latitude upwelling of molecularspecies increases the plasma loss rate, so that strong heating during magneticstorms can result in electron-density depletions that are a part of ionosphericstorm phenomena.

250

Figure 9. Schematic of the thermospheric compositional response to geomagnetic storms as afunction of latitude at various times during the storm. The ratio is storm-time departure rela-tive to geomagnetically quiet conditions. (From Roble, 1977).

7. Gravity Waves and TidesAtmospheric observations reveal a wide variety of wave motions, from short-

period and small-scale sound waves to long-period and global-scale planetarywaves. The exponential decrease in atmospheric density with increasing heighttends to be accompanied by growth in the amplitude of velocity and temperatureperturbations associated with the waves, so that large wave amplitudes are com-monplace in the thermosphere. The main thermospheric wave motions are \itgravity waves with periods from a fraction of an hour to several hours, and \itatmospheric tides with periods around 12 hours and 24 hours. Gravity waves areof interest because of information they provide about transient atmosphericprocesses that generate them, and because of their potential to transport momen-tum and energy between different atmospheric layers. Tides are the dominantform of wind in the lower thermosphere, and they impact the dynamics of theentire thermosphere and ionosphere.

251

Gravity waves with periods longer than about 1/2 hour are approximately inhydrostatic balance, and thus satisfy Eq. 12, 18, 35, and 44. To understand thebasic properties of such waves, let us work with linearized versions of thoseequations by making replacements like:

H → H0 + H ’ (53)

and dropping all quantities of quadratic or higher order involving the primedterms.

For simplicity, let us also neglect viscosity, heat conduction, diffusion, theCoriolis acceleration, mean winds [ i.e., v0 ], and gradients of m, cp, and g. Thelinearized equations are then:

∂ Φ ’ ∂ Z

- g H ’ = 0 (54)

∂ W ’ ∂ Z

- W ’ + p . vh’ = 0 (55)

∂ vh’

∂ t + p ’ =

J x B ρ

(56)

g ∂ H ’ ∂ t

+ H02 N2 W ’ = k

m cp Q ’ (57)

where the angular "buoyancy frequency", N, also called the angular Brunt-Väisäläfrequency, is defined by:

N2 = g

H0

k

m cp + ∂ H0

∂ z . (58)

The dimensionless quantity k / ( m cp ) is 2 / 7 for an atmosphere that is pre-dominantly N2 and O2, and 2 / 5 for an atmosphere that is predominantly O. N isthe natural frequency at which air parcels undergoing vertical adiabatic motiontend to oscillate owing to buoyancy forces. Typical values of the buoyancy period2 π / N are listed in Table 1.

The terms on the right-hand sides of Eq. 56 and 57 can be considered as sourceterms. In the thermosphere, the Amp\‘ere force and Joule heating caused byauroral electric currents can produce gravity waves that have been observed totravel a good fraction of the Earth’s circumference. However, most of the gravitywaves observed in the thermosphere appear to originate from the lower atmos-

252

phere, where the source can be latent heat release, non-linear dynamical phenom-ena neglected in Eq. 54 - 57, or other processes.

Outside of source regions the right-hand sides of Eq. 56 and 57 vanish, and wecan examine the solution for a monochromatic wave that varies in time and in thehorizontal x-direction as:

exp( i ω t - i κ x ) (59)

where i is -1, κ is the horizontal wavenumber and ω is the angular frequency.The horizontal phase trace velocity of the wave is

vpx = ω κ (60)

which is in the positive x direction when ω and κ have the same sign.

Equations 54 - 57 yield:

∂ Φ ’ ∂ Z

- g H ’ = 0 (61)

∂ W ’ ∂ Z

- W ’ - i κ vx’ = 0 (62)

i ω vx’ - i κ Φ ’ = 0 (63)

i ω g H ’ + H02 N2 W ’ = 0 (64)

If H0 is assumed to be constant with height, Eq. 61 - 64 have nontrivial solu-tions in which the primed variables vary with altitude as:

exp

1 2 ± i K Z (65)

where K is a dimensionless vertical wavenumber given by

K = 1 2

κ2 C2

ω2 - 1

½

= 1 2

C2 vpx2 - 1

½

(66)

C ≡ 2 H0 N (67)

C has the units of velocity, and for an isothermal atmosphere is a little underthe speed of sound.

253

When vpx < C, K is real, and the solutions have a propagating oscillatory

structure in the vertical, with a wavelength of 2 π H0 / K. Such waves are called

internal gravity waves, and C is their limiting speed. If ω is positive, the solutionwith the plus sign in Eq. 65 has downward phase propagation, while that with theminus sign has upward phase propagation. When vpx > C, K is imaginary, and thesolutions have an exponential structure in the vertical. Both the propagating andthe exponential solutions have a factor proportional to exp( Z / 2) that causes theamplitude to grow with increasing altitude, unless such growth is overwhelmed bya large imaginary K. Thus upward propagating waves can attain large amplitudesin the thermosphere. Conversely, waves propagating downward have their ampli-tudes exponentially suppressed, so that waves generated in the upper atmosphereare difficult to detect at lower altitudes.

Typical values of C at different altitudes are listed in Table 1. Because C gen-erally varies with height, K also varies with height, and Eq. 65 does not strictlyrepresent the vertical structure of the waves. However, if K varies sufficientlyslowly with height and does not approach zero, then approximate solutions toEq. 61 - 64 can be found which have an exponential dependence as:

exp

⌡⌠

z0

z

1 2 ± i K ( Z ’’) d Z ’’ (68)

These solutions are still wave-like with respect to height when K is real, but thewavelength varies with height. Regions where K approaches zero will tend toreflect propagating waves.

The vertical [upward] phase trace velocity of an internal wave is

vpz = ± ω H0

K (69)

with the upper or lower sign corresponding to the upper or lower sign in Eq. 65 or68.

The group velocity, which gives the velocity with which the energy in a wavepacket would travel, is found by differentiating ω with respect to κ and K, usingthe dispersion relation Eq. 66. Solving Eq. 66 for ω2 gives:

ω2 = κ2 C2

4 K2 + 1 (70)

The horizontal component of group velocity is:

254

Figure 10. Contributions to the wave energy dissipation rate coefficient due to moleculardissipation and to ion drag. For molecular dissipation the coefficient is shown for two dif-ferent horizontal wave phase velocities vpx (represented by u here): 300 m.s-1 and 600 m.s-1.

For ion drag the coefficient is shown for typical (not extremum) day and night conditions.(From Richmond, 1978).

vgx = ∂ ω ∂ κ =

ω κ

= vpx (71)

The vertical component of group velocity is:

vgz = _+ H0

∂ ω ∂ K

= ± H0 ω

K 4 K2

4 K2 + 1 = - 4 K2

4 K2 + 1 vpz (72)

which has the opposite sign of the vertical phase trace velocity and is smaller inmagnitude, although the magnitudes become similar when K is large in compari-son with 1/2.

Gravity waves can be generated at all heights in the atmosphere, but the energyavailable for generation generally decreases with increasing altitude. At any givenaltitude in the upper atmosphere most of the wave energy usually comes fromlower levels, and so most observable waves have upward group velocities. Sincethe vertical group and phase velocities have opposite signs, the phase propagationof these waves is usually downward.

Dissipation of gravity waves in the thermosphere arises from ion drag, viscos-ity, and heat conductivity. The characteristic rates for ion drag and viscosity listedin Table 1 are indicative of the importance of those effects; for viscosity, the ratesare appropriate for waves with a vertical wavelength of 2 π H. The characteristic

255

dissipation rate due to molecular heat conduction is about 1.5 times that due tomolecular viscosity. For both of these molecular processes, the characteristic rateis approximately proportional to the inverse square of the vertical wavelength.From the dispersion relation Eq. 66, it can readily be seen that waves with shortvertical wavelengths are those with horizontal phase speeds that are slow incomparison with C. Thus slow-moving waves tend to be rapidly dissipated as theypropagate into the upper thermosphere. Figure 10 shows representative gravity-wave dissipation rates due to ion drag and to molecular processes, the latter fortwo different horizontal phase trace speeds vpx [labeled u in the figure].

The primary way in which gravity waves imprint their signature on the iono-sphere is through the vertical plasma motions they can induce. A gravity waveproduces undulations in the ionosphere that propagate with the phase velocity ofthe wave. These are known as Traveling Ionospheric Disturbances [TIDs]. Fig-ures 11 and 12 show examples of the manner in which the ionospheric undula-tions propagate horizontally and vertically.

Waves that propagate from the lower atmosphere into the thermosphere musthave horizontal phase velocities less than the value of C in the mesosphere, whichTable 1 shows to be around 230 m.s-1. Higher-speed waves become evanescent,and so that value can be considered as a high-speed cutoff for wave penetration.[Background winds and temperature variations can cause the value of the cutoffto vary by about ± 25 %]. By contrast, waves that are generated by auroral electriccurrents and that propagate into the upper thermosphere can have much largerphase speeds, on the order of 800 m/s, since these waves are generated within ascale height or so of 130 km, where the value of C is large. Thus the observedphase speed of a TID gives a clue about its possible source: TIDs moving fasterthan 350 m/s are unlikely to originate in the lower atmosphere, while thosemoving slower than 200 m.s-1 may very well have a lower-atmospheric source.

Figure 11. Backscattered power from a north-looking beam of the Goose Bay Radar on 1988November 25. The streaks show the effects of equatorward-propagating traveling ionosphericdisturbances. (From Samson et al., 1990).

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Figure 12. Variations of ionospheric virtual heights (radar pulse delay divided by twice thespeed of light) at different radar frequencies (in Mhz). A wave feature with a mean period ofaround 35 min and downward-propagating phase features is apparent at all heights. (FromGeorges, 1968).

Atmospheric tides are global oscillations with periods of one solar or lunar day,or some integral fraction thereof. Solar tides are the dominant form of wind in thethermosphere. Tides have many of the characteristics of gravity waves, such asamplitude growth with altitude and downward phase propagation in the presenceof upward energy propagation. In fact, tides can be described by the same equa-tions as gravity waves, Eq. 54 - 57, with the addition of Coriolis acceleration toEq. 56. However, the variation of the Coriolis parameter f with latitude means thatplane-wave solutions of the form Eq. 59 are not possible. Rather, discrete modesappear as possible solutions, at least in a horizontally arises from the requirementthat solutions be continuous around the Earth. Although the variation of a mode inlongitude is simply sinusoidal, the variation in latitude is more complex. Whenrealistic latitudinal variations of atmospheric temperature and mean zonal windsare taken into account, the latitudinal and vertical structures of the tidal modesbecome coupled. Nevertheless, wavelike features in the vertical structure remain.The main source of solar tides is the daily variation of solar radiation absorbed byoxygen in the thermosphere, by ozone in the stratosphere and mesosphere, and bywater vapor in the troposphere. Lunar tides are driven by lunar gravitationalforcing, and have amplitudes typically only a few percent those of solar tides.Upward-propagating tides are clearly visible in the lower thermosphere: at highlatitudes, semidiurnal [12-hour] tides are usually strongest, while at low latitudes,both semidiurnal and diurnal [24-hour] tides are important. Figure 13 shows thedaytime wind in the lower thermosphere on three days in August, 1974, above theArecibo incoherent-scatter radar.

The slow downward progression of eastward and westward wind regimes areclearly evident, associated primarily with the tides.

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Figure 13. Eastward component of the neutral wind above Arecibo, Puerto Rico, for 10, 12,and 13 August 1974. Contour levels are 20 m.s-1, and shaded contours show westward winds.(From Harper, 1977).

8. Dynamo Effects of Thermospheric WindsWinds contribute to the electric current through the so-called "dynamo electric

field" v x B in Eq. 30, which is the electric-field component associated with thetransformation from the Earth-based reference frame to the reference framemoving with the wind. As in an electric dynamo, an electromotive force is createdas the conducting medium is moved through the magnetic field. The electric fieldE in the Earth-based reference frame is influenced by dynamo effects, becausedivergent current driven by the dynamo electric field creates space charge thatresults in a polarization electric field. The current must be divergence-free in threedimensions, and the large-scale electric field is normally electrostatic, withnegligible geomagnetic-field-aligned component:

. J = 0 (73)

E = - Φe (74)

E// = 0 (75)

where Φe is the electrostatic potential.

Equations 74 and 75 require that geomagnetic field lines be equipotentials. Athigh latitudes, Equation 73 effectively relates the geomagnetic-field-alignedcurrent density at the top of the conducting ionosphere to the height-integratedhorizontal ionospheric current density. That is, current must flow into or out ofthe top of the ionosphere from the magnetosphere in order to balance any diver-gence or convergence of the horizontal current.

When Ohm’s Law Eq. 30 is used to replace J⊥ in Eq. 73, it can be seen thatthe field-aligned current is related both to the electrostatic field E and to the

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dynamo field v x B. It was noted in Section 5 that the wind in the high-latitudeF-region tends to have a pattern with some similarity to the electrodynamicconvection velocity ue (= E x B / B2) that is produced largely by magneto-spheric processes. The similarity becomes less at lower altitudes, where thecharacteristic rate associated with ion drag is slower. As a result, v x B has sometendency to be directed opposite to E, but to have a weaker magnitude. Conse-quently, the field-aligned current associated with v x B tends to be opposite to,but weaker than, that associated with E. Figure 14 shows an example of theelectric-field-driven and wind-driven field-aligned current distributions at the topof the ionosphere from a simulation with the NCAR TGCM. Note that the scalesfor the two components are different, since the wind-driven current is considera-bly weaker. The tendency for anticorrelation of the two current components isevident.

Figure 14. Components of the field-aligned current density for 1992 March 29, 09:00 UT,over northern latitudes above 42.5$° geographic, estimated with the Assimilative Mapping ofIonospheric Electrodynamics (AMIE) procedure and the NCAR Thermosphere-IonosphereGeneral Circulation Model (TIGCM). Local noon is at the top. (Left) Current driven by theelectric field (contour interval 0.2 µA.m-2. (Right) Current driven by the dynamo effect ofthermospheric winds (contour interval 0.04 µA.m-2). Solid contours are downward current;dashed contours are upward current. (From Lu et al., 1995).

There are indications that the magnitude and direction of the electric field ongeomagnetic-field lines that are open to the solar wind, in the polar cap, arerelatively insensitive to ionospheric conditions; i.e., the magnetosphere tends toact as a voltage generator. At those latitudes, it is appropriate to consider thethermospheric winds as tending to reduce the strength of the field-aligned cur-rents, without affecting the electric field, as in the example above. However, atlower latitudes where geomagnetic-field lines are closed, it is not always possible

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for the magnetosphere to absorb changes in the field-aligned current and stillmaintain current continuity. Instead, the electric field may change in a way thattends to preserve the field-aligned current density. In simplified terms, the mag-netosphere can be considered to act as a current generator rather than a voltagegenerator. Figure 15 illustrates how the electric field can be modified by thewinds.

Figure 15. Results of a TIE-GCM simulation illustrating the "flywheel" effect for solar-minimum equinox conditions. Contour intervals are 1000 V; vector velocity scales vary, asshown at the lower right of each plot. (a) Electric-potential contours and ion-drift vectors ingeographic coordinates between 47.5° and the North Pole, at 00:00 UT, for a diurnally re-producible simulation with an imposed cross-polar-cap potential of 30 kV. (b) Correspondingneutral wind vectors at 145 km altitude. (c) Electric potential contours and ion-drift vectorsone time-step later, after field-aligned current between the ionosphere and the outer magne-tosphere has been cut off. (From Richmond, 1995a).

This time, a modified version of the NCAR TGCM is used, the Thermosphere-Ionosphere-Electrodynamics General Circulation Model [TIE-GCM]. The TIE-GCM calculates the ionospheric-dynamo effects of thermospheric winds, andconsiders self-consistently the feedback of the dynamo electric fields and currentson the neutral dynamics. Figure 15a shows the imposed electric potential and the

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ion-drift velocities for a steady-state simulation, while Figure 15b shows the windat 145 km, an altitude that is representative of the height-averaged dynamo ef-fects. Figure 15c shows the electric potential and ion drifts one time step later,after the field-aligned currents to the outer magnetosphere have artificially beencut off. The pattern is somewhat similar to that in Figure 15a, except for beingweaker and rotated about two hours in local time. This electric-potential patterncan be considered to be that component produced by the ionospheric dynamo ifthe magnetospherically imposed currents are not allowed to change, contrary tothe simulation of Figure 14. The tendency for the wind-produced ion convectionto have the same pattern as magnetosphere-produced convection has been calledthe "flywheel" effect. That is, the inertia of the neutral winds can be considered tohelp maintain the ion convection imposed by the magnetosphere. The fact that thepattern is rotated in local time can be attributed to the inertia of the winds in thepresence of the Earth’s rotation.

Acknowledgments.

I thank Gang Lu for helpful comments on the manuscript. The National Center for Atmosphe-ric Research is sponsored by the National Science Foundation. This work was partly suppor-ted by the NASA Space Physics Theory Program.

9. ReferencesBrinkman D.G., R.L. Walterscheid, A.D. Richmond, and S.V.

Venkateswaran, Wave-mean flow interaction in the storm-time thermo-sphere: a two-dimensional model simulation, J. Atmos. Sci., 49, 660-680,1992.

Georges T.M., HF doppler studies of travelling ionospheric disturbances, J.Atmos. Terr. Phys., 30, 735-746, 1968.

Hargreaves J. K., The solar-terrestrial environment, Cambridge Univ. Press,Cambridge, 1992.

Harper R.M., Tidal winds in the 100-200 km region at Arecibo, J. Geophys.Res., 82, 3243-3250, 1977.

Hedin A.E., MSIS-86 thermospheric model, J. Geophys. Res., 92, 4649-4662,1987.

Holton J.R., An Introduction to Dynamic Meteorology, Academic Press, NewYork, 1979.

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Kelley M. C., The Earth’s Ionosphere: Plasma Physics and Electrodynamics,Academic Press, San Diego, 1989.

Lu G., A.D. Richmond, B.A. Emery, and R.G. Roble, Magnetosphere-ionosphere-thermosphere coupling: effect of neutral wind on energy transferand field-aligned current, J. Geophys. Res., 100, 19,643-19,659, 1995.

Rees M. H., Physics and Chemistry of the Upper Atmosphere, Cambridge Univ.Press, New York, 1989.

Richmond A.D., Gravity wave production, propagation, and dissipation in thethermosphere. J. Geophys. Res., 83, 4131-4145, 1978.

Richmond A.D., Thermospheric dynamics and electrodynamics, in Solar-Terrestrial Physics, Principles and Theoretical Foundations, (R.L. Carovil-lano and J.M. Forbes, eds.), D. Reidel Publishing Company, Dordrecht, Hol-land, 523-607, 1983.

Richmond A.D., The ionosphere, in The Solar Wind and the Earth, (S.-I. Aka-sofu and Y. Kamide, eds.), Terra Scientific Publishing Company, Tokyo,123-140, 1987.

Richmond, A.D., The neutral upper atmosphere, in Geomagnetism and Aero-nomy, (J.A. Jacobs, ed.), 4, 403-479, 1991.

Richmond A.D., The ionospheric wind dynamo: effects of its coupling withdifferent atmospheric regions, in The Upper Mesosphere and Lower Thermo-sphere, edited by R. M. Johnson and T. L. Killeen, pp. 49-65, Am. Geophys.Union, Washington, DC, 1995a.

Richmond A.D., Ionospheric electrodynamics, in Handbook of AtmosphericElectrodynamics, Vol. II, edited by H. Volland, pp. 249-290, CRC Press,Boca Raton, Florida, 1995b.

Roble R.G., The thermosphere, in The Upper Atmosphere and the Magneto-sphere, pp. 57-71, NAS Press, Washington, D.C., 1977.

Roble R.G., The Earth’s thermosphere, in The Solar Wind and the Earth, editedby S.-I. Akasofu and Y. Kamide, pp. 245-264, Terra Sci. Pub. Co., Tokyo,1987.

Roble R.G., J.M. Forbes, and F.A. Marcos, Thermospheric dynamics duringthe March 22, 1979 magnetic storm, 1. Model simulations, J. Geophys. Res.,92, 6045-6068, 1987.

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Samson J.C., R.A. Greenwald, J.M. Ruohoniemi, A. Frey, and K.B. Baker,Goose Bay Radar observations of Earth-reflected atmospheric gravity wavesin the high-latitude ionosphere, J. Geophys. Res., 95, 7693-7709, 1990.

U.S. Standard Atmosphere, U.S. Gov. Printing Off., Washington, D.C., 1976.

Volland H., Atmospheric Tidal and Planetary Waves, Kluwer Academic Pub-lishers, Dordrecht, Netherlands, 1988.

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RADAR OBSERVATIONS OF THE MIDDLE AND LOWERATMOSPHERE

Jürgen Röttger

1. IntroductionScatter and reflection of electro-magnetic waves from irregularities in the

refractive index of the Earth’s atmosphere has been a very essential researchsubject in radio science. Total reflection of high frequency waves was the majormechanism to study the ionosphere with the traditional ionosondes. Forward andbackscattering from atmospheric and ionospheric irregularities was found athigher frequencies and, after the invention of the radar technique, have becomemost effective means to study the atmosphere and ionosphere. The incoherent orThomson scatter radars as well as the mesosphere-stratosphere-troposphere [MST]radars have proved very essential for the studies of the Earth’s environment from afew kilometers to more than 1000 km altitude. Many review papers on the theory,the techniques and the achieved results exist [Gage and Balsley, 1980; Mathews,1984; Hocking, 1985; Collis and Röttger, 1990; Röttger and Larsen, 1990;Röttger and Vincent, 1996]. These references deal essentially with coherent andincoherent scatter of the middle and lower atmosphere. Coherent scatter radars areused in addition to study irregularities in the ionospheric E- and F-region [e.g.,Crochet et al., 1979; Greenwald, 1996].

Mesosphere-stratosphere-troposphere [MST] radars, which are the main subjectof this paper, are particularly used for studies of the dynamics of the middle andlower atmosphere. The scattering and reflection process from atmospheric andionospheric irregularities in the refractive index, which lead to the radar echoes, isstill not fully revealed, since the actual structure of the irregularities causing MSTradar echoes is very difficult to measure. However, it is certain that particular at-mospheric characteristics, such as relevant information on the structure and dyna-mics [e.g., Gage, 1990], can be uniquely determined by the MST radars, whichmake their applications invaluable for lower and middle atmosphere research.These applications as well as the studies of the scattering/reflection mechanismsand the originating inhomogeneities and irregularities, and the research of thestructure and dynamics of this atmospheric region remain as challenging tasks.

After recapitulating some categories of radars used to study the ionosphere andthe atmosphere, the incoherent scatter and MST radar scatter processes are brieflyintroduced in order to exhibit the transition between these two processes, whichtakes place in the mesosphere. Then the features of the transition fromcoherent to incoherent radar scatter are discussed. Thereafter we concentrate on

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Radar Methods for Investigations of the Lower and Middle Atmosphere and theThermosphere/Ionosphere

Typical operation parameters (approximate)

Radar Method FrequencyRange

Wavelength in m

AveragePowerin kW

AntennaDimension

inWavelengths

HeightRegion

MF Radar MF-HF 150-50 0.01-1 1-10 M,LT/Io

HF Radar* HF 300-10 0.01-5 0.5-1 Th/Io

CoherentRadar^

HF-VHF 30-1 0.1-1 5-50 Th/Io

Meteor Radar HF-VHF 10-6 0.1-10 2-10 M,LT

MST Radar VHF 6-7 1-100 5-50 M,S,T

IncoherentScatter Radar VHF-UHF 6-0.25 100-300 100-300 M,LT/Io

ST Radar VHF-SHF 6-0.1 1-500 10-500 S,T

BL Radar UHF 0.3 0.01-0.1 10 T

MF = 0.3-3.0 MHz M = MesosphereHF = 3.0-30 MHz S = Stratosphere

VHF = 30-300 MHz T = TroposphereUHF = 300-3000 MHz LT = Lower ThermosphereSHF = 3-30 GHz Th/Io = Thermosphere/Ionosphere

* = Ionosonde ^ = Irregularity ScatterTable 1. Radar methods for investigations of the lower and middle atmosphere and thethermosphere/ionosphere and typical operation parameters.

the scattering and reflection mechanism of the MST radar echoes, and discuss afew common techniques applied with these radars. Some troposphericobservations with the EISCAT UHF radar are described. Examples of polar meso-sphere echoes, recorded with the EISCAT VHF radar, are then briefly addressed,together with a short synopsis of potential mechanisms causing these echoes.Finally justifications for using the EISCAT Svalbard Radar in combination with adedicated MST radar for studies of the middle and lower atmosphere in polarregions are outlined.

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This article is a composition of several tutorials and reviews the author hadpresented during the recent years, which partially had been published atdiversified places [see: Röttger in list of references]. It was attempted in thissummary article to combine these presentations and adjust the chapters in a mostlogical way, although it is admitted that this may not have been successfullyachieved everywhere. To cover such a broad context, it has been tried, though, toarrange the chapters that most of them can also be read as stand-alone discourses.

The literature in this field has become quite superfluous and cannot at all bereproduced in the list of references here. Only essential reviews and tutorials,puplished in the past 10-15 years, and source references of the initial work as wellas of presented diagrams and tables are included in the attached list of references.Readers are also referred to several Handbooks of MAP [see: certain references tothese handbooks], and special issues of Radio Science published in 1980, 1985,1990, 1995 and 1997 following the Workshops on Technical and ScientificAspects of MST Radar. Some papers on D-region studies with the EISCATincoherent scatter radars can be found in the special issues of the Journal ofAtmospheric and Terrestrial Physics of 1983, 1985, 1987, 1989, 1991, 1993 andAnnales Geophysicae in 1996, which followed the EISCAT Workshops. The mostrecent review on advances in radar techniques for studies of the MST region iswritten by Hocking [1997], and Cho and Röttger [1997] summarised the status ofobservations and theory of Polar Mesosphere Summer Echoes and their relation toNoctilucent Clouds.

2. Ionospheric and Atmospheric RadarsRadars operating in the frequency ranges from MF [medium frequency] to UHF

[ultra-high frequency] are used to investigate the structure and dynamics of thetroposphere, stratosphere, mesosphere, the ionosphere and the thermosphere, aswell as even the exosphere. In Table 1 the different kinds of such radars aresummarised, together with typical operation parameters and the observablealtitude regions.

The HF radars, either modern digital ionosondes [e.g., Reinisch, 1996]irregularity scatter radars [e.g., Hanuise and Crochet, 1977; Greenwald, 1996],are applied for E- and F-region studies, also UHF radars are occasionally used forthis purpose. These coherent scatter radars are often just called coherent radars.The term coherent is used here in order to discriminate between the incoherentscatter and the coherent scatter processes, responsible for these observations. Thedigital ionosondes are useful complements to study the electron density profiles inthe upper D-region and the E-region such as during sporadic-E events, to calibrateincoherent scatter radar electron density profiles and to measure drift velocitiesand incidence angles.

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MF radars, making use of partial reflection from electron density inhomogene-ities, are particularly applied to measure electron density profiles of the iono-spheric D-region as well as the horizontal wind velocity in this altitude range,comprising the mesosphere. The partial reflection method is applied to measureelectron densities as function of height in the ionospheric D-region and alsoallows to deduct the collision frequency between ions and neutrals. The ex-periment uses MF or HF radars in the frequency range of about 2-6 MHz. Theordinary and extra-ordinary components of the radar wave, which is partially re-flected from D-region electron density irregularities, are attenuated differently.Comparing the amplitudes of these components, the electron density profile isdeduced. This method, which is also called the differential absorption technique,was successfully applied for more than thirty years. A summary description andhistory of this development, which began decades ago, can be found in Röttgerand Vincent [1996].

This principle partial reflection or scattering mechanism is also used by radarsoperating in the same frequency range of the MF or low HF bands to measuremesospheric and lower thermospheric turbulence and wave structures [Hocking,1987]. It is also extensively applied to measure wind velocities by means of thespaced antenna correlation technique [Briggs, 1980, 1984]. This method is alsocalled partial reflection drift technique using MF radars. More recently the namemesosphere-lower thermosphere [MLT] radars has been introduced [Manson etal., 1990], since it has become one of the major tools to continuously observewinds, tides and gravity waves in this altitude region. Certain extensions of thistechnique have been introduced, such as the Imaging-Doppler-Interferometer[IDI] technique [Adams et al., 1985], which is applied to measure winds as well asincidence angles and aspect sensitivity of partially reflected MF radar echoes fromthe mesosphere.

The meteor radar technique is one of the oldest to study upper mesosphere pro-cesses. Radar echoes scattered from ionised meteor trails, which drift under theaction of the neutral wind, are analysed. By measuring the line-of-sight Dopplervelocity, the range of the echo and its arrival angle the wind profile is computed[Roper, 1984]. The meteor radar observations agree well with simultaneousincoherent scatter radar and MST radar observations. Mean winds and tides bet-ween about 80 km and 100 km altitude have been deduced with this technique atmany places on the globe. Since the optimum frequencies of the meteor radars arein the range of the MST radars around 30-70 MHz, some of these MST radars havebeen actively or passively used for meteor radar applications.

The mesosphere-stratosphere-troposphere [MST] radars, operating in the lowerVHF band, usually near 50 MHz, detect echoes from turbulence-inducedirregularities and gradients of the radio refractive index [Woodman and Guillen,

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1974]. These radars are applied to investigate winds, waves, turbulence andstability in the indicated altitude regions. The turbulence can be in the clear or thecloudy air. The smaller versions of the MST radars, covering only the lower stra-tosphere and the troposphere altitudes, are called ST radars. These radars are alsooperated in the UHF and SHF bands [Woodman, 1980a,b; Gage, 1990].Operational applications of ST radars have developed in the last decade, and suchST radars are then called wind profilers [Gage, 1990; Röttger and Larsen, 1990;Czechowsky, 1994].

Incoherent scatter [also known as Thomson scatter] radars, making use ofscatter from free electrons in the ionospheric plasma, are applied to study the io-nosphere, and thus the mesosphere and thermosphere as well as the exosphere[Mathews, 1984; Hagfors, this issue].

For studies of meteorological phenomena the weather radars, detecting echoesfrom precipitation [rain, snow and hail], are normally operated in the SHF bandsabove a few GHz. These latter radars will not be discussed here, and details canfor instance be found in the books by Battan [1973], Gossard and Strauch [1983],Doviak and Zrnic [1984] and Sauvageot [1992]. Also echoes from lightning arenot discussed here and reference is made to Williams et al. [1990], who reviewedthe observations at UHF and SHF, and Röttger et al. [1995], who presented thefirst VHF ST radar observations of lightning echoes.

3. Scattering Properties of incoherent scatter and MSTradars

A schematic view of the different mechanisms causing scattering and reflectionof electro-magnetic waves in the troposphere, stratosphere, mesosphere andthermosphere/ionosphere are represented in Tables 2a and 2b [Röttger andVincent, 1996]. In the ionised part of the atmosphere [Table 2a], namely theionosphere, the reflection of radio waves is determined by the electron density,defining the plasma frequency fN. For radio waves of frequency f = fN total reflec-tion occurs. This allows the height profile of electron density to be determined, asit is traditionally done with ionosondes [sometimes also called HF radars]. Forf > fN, and if there is a vertical gradient or irregularities in electron density,partial reflection occurs, which is used with the MF radars.

When the operating frequency f is much higher than the plasma frequency, i.e.f » fN , scattering of radio waves takes place. This scattering process in the iono-sphere can primarily be due to two different contributions:

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Table 2. (a: left) Scattering and reflection from refractive index variations of the atmosphere,resulting in total or partial reflection and incoherent (Thomson) scatter; (b: right) Scatteringand reflection from irregularities of the refractive index due to plasma and neutral airturbulence or stable structures in the clear air.

a) random thermal motions of electrons and ions cause "incoherent" scatter[see: Hagfors, this issue], which is also called "Thomson scatter", since itresults from the collective Thomson scattering of the free electrons in the radarvolume,

b) different kinds of plasma instabilities, generated either by natural [Fejer andKelley, 1980] or artificially [by ionospheric heating: Rietveld et al., 1993]generated instabilities can cause plasma waves and plasma turbulence whichresult in a direct perturbation of the ionisation.These perturbations are known as E- and F-region irregularities. They cause

scattering and partial reflection of MF, HF, VHF and UHF signals. Well knowninstruments to study these irregularities and the corresponding ionospheric dyna-mics are the auroral or equatorial electrojet radars, for instance [e.g., Fejer andKelley, 1980]. Also F-region irregularities are observed at high latitudes withobliquely beaming HF radars [Greenwald, 1996]. Usually, these backscatterprocesses are highly anisotropic with the maximum scatter cross section occurringperpendicular to the Earth’s magnetic field direction. Artificial PeriodicInhomogeneities, created by standing wave pattern during ionospheric heatingexperiments also cause scattering and can be used for diagnostics of the

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mesosphere [Belikovich et al., 1986]. The EISCAT heating facility was used forthis purpose [Goncharov et al., 1993].

With respect to the neutral part of the atmosphere [Table 2b], it is establishedthat the refractive index n is almost equal to one for radio waves in the HF, VHFand UHF bands. In the neutral atmosphere dynamic and convective instabilitiescause clear air turbulence, which result in a perturbation of humidity, temperatureand density. Mixing of different air masses and inversion layers also causediscontinuities of these parameters. The corresponding irregularities in therefractive index, which can randomly vary due turbulent velocity fluctuations orprevail as stably stratified layers, scatter or partially reflect radar signals,respectively.

Clear air turbulence in the mesosphere results in a perturbation of the ionisation[D-region irregularities]. It should be noted that these irregularities are notcreated by plasma instabilities, but are induced by neutral air turbulence due to thehigh collision frequency between molecules and ions. These D-region irregu-larities are therefore regarded in a first approach as replica of structures in theneutral atmosphere, and they are not aligned along the Earth’s magnetic field. It isalso accepted that chemical and hydration processes cause ionisationperturbations in the D-region. Considerable refractive index changes due to thesemesosphere irregularities can occur for radar signals in the low VHF band, whichis made use of by the MST radars.

3.1. Some Basics of Incoherent Scatter [IS] from the D-regionA very appropriate addition to these kinds of radars for studies of the lower iono-

sphere, the mesosphere and the regions above are the Thomson scatter radars,which are customarily called incoherent scatter radars. These IS [incoherent scatter]radars are used to observe backscatter from the ionosphere. The scatter cross sec-tion of incoherent scatter is usually much smaller than the one of "turbulence"scatter detected by MST radars.

Up to altitudes of the lower thermosphere and the upper mesosphere [around90-100 km], the ionosphere is governed by collisions of the ions with neutralmolecules. At these altitudes, in the collision dominated regime of incoherentscatter, the plasma temperature and ion-neutral collision frequency [neutral den-sity] can be deduced from the spectra of the scattered signals in addition to theelectron density and the ion [neutral] velocity. From the spectral width certaindeductions of ion composition can be obtained, such as for instance the negativeion density and the ion mass. Mathews [1984] has reviewed the incoherentscattering from the collision dominated D-region and pointed out that this method

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offers a unique advantage in inferring mesospheric parameters with very high pre-cision, such as for example the ratio of the neutral number density and the neutraltemperature. However, ion chemistry, i.e. negative and positive ions, have also tobe carefully considered [Turunen, 1996].

Figure 1. (a: top panel) Height-time contour plot of electron density measured with theEISCAT UHF (931 MHz) incoherent scatter radar during energetic particle precipitation.The maximum electron density was 8x1010 m-3, the spacing between two contour levels corre-sponds to a factor of √2. (b: middle panel) Height-time-intensity plot of polar mesospheresummer echoes (PMSE), measured with the EISCAT VHF (224 MHz) radar. The peak level is16 dB above the noise level; (c: bottom panel) Height-time contour plot of mesosphere echoesin winter measured with the SOUSY VHF (53.5 MHz) radar at polar latitudes (Rüster andKlostermeyer, 1987).

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Figure 2. First backscatter power profile obtained from fluctuations of the refractive index inthe mesosphere, stratosphere and troposphere, measured with the 50-MHz radar atJicamarca, Peru (Woodman and Guillen, 1974).

The incoherent radars mostly operate in the VHF and UHF band at frequenciesbetween 50 MHz and 1300 MHz. There exist only a few incoherent scatter radars,such as the Jicamarca radar in Peru, the Arecibo Observatory on Puerto Rico, theMillstone Hill radar near Boston, USA, the Sondrestromfjord radar in Greenland,the MU radar in Japan and the EISCAT radars in northern Scandinavia and onSvalbard [see Röttger, 1989; and Hocking, 1997; for a detailed lists]. More recentlyradars in Russia and the Ukraine were known to observe the ionosphere with the in-coherent scatter technique. The Jicamarca radar and the MU radar are also used asMST radars due to their low operating frequency around 50 MHz. The IS radars inArecibo and Millstone Hill [430 MHz], EISCAT [930 MHz] and Sondreström [1.3GHz] are also used for troposphere and stratosphere observations.

The transmitter power of IS radars is usually higher than one megawatt and theantenna gains are substantially larger than those of the MST radars. Altitude resolu-tions are typically in the range of a few hundred meters to some kilometers or moreand time resolutions can be as good as 10 seconds but have to be up to several 10minutes depending on the signal-to-noise ratio and the temporal variation of the ob-served processes. The lowest altitude from which IS radars obtain echoes is around55 - 60 km, depending on the radar power and antenna area, and of course theelectron density.

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Due to viscous subrange limitations in the mesosphere [Hocking, 1985], whenneutral turbulence fluctuations are very strongly damped at the scales corre-sponding to the IS radar wavelengths of less than some meters, the IS radars areusually supposed to be insensitive to "turbulence scatter" from the mesosphere.However, turbulent fluctuations and the corresponding eddy diffusion starts todominate molecular diffusion in the mesosphere. The interpretation of incoherentscatter spectra then becomes ambiguous depending on which type of diffusiondominates the scattering mechanisms.

An example of a height-time-intensity diagram of incoherent scatter echoes isshown in Figure 1a. These short-lived electron density enhancements are frequentlydetected with the EISCAT radars, operated on 931 MHz and 224 MHz in the auroralregion [Röttger, 1991]. High energy particles from the magnetosphere penetratedown into the mesosphere, where they cause such enhancements of the electrondensity. In summer even stronger echoes are detected around the mesopausealtitude, which are shown in Figure 1b [Röttger et al., 1990]. These polar meso-sphere summer echoes [PMSE] result from irregularities, which are related toaerosols and ice particles in the low-temperature mesopause, which will be brieflydiscussed in a later chapter. In Figure 1c backscatter echoes observed on 53.5 MHzare shown, which are related to the background electron density in the mesospherebeing perturbed by neutral turbulence as will be discussed now.

Figure 3. Height-time contour plot of mesosphere radar echoes measured with the MU (46.5MHz) radar in mid-latitudes in Japan (Sato et al., 1985).

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3.2. Some Basics of the Mesosphere-Stratosphere-Tropos-phere [MST] Radar

The technique of using sensitive clear-air radars to investigate the upper atmo-sphere at altitudes from the troposphere to the mesosphere owes much of its successto the early days of ionospheric incoherent backscatter observations. It was foundthat radars operating in the low VHF band [≈ 50 MHz] also produce echoes from themiddle and lower atmosphere in addition to those from the ionosphere. Woodmanand Guillen [1974] used the incoherent scatter radar at the Jicamarca Radio Obser-vatory in Peru and were the first to analyse such echoes from the mesosphere andthe stratosphere. The first power profile obtained by backscatter from fluctuations inthe refractive index in the clear air of the mesosphere and the stratosphere is presen-ted in Figure 2. Woodman and Guillen [1974] showed that these strong echoes arenot due to incoherent scatter but caused by turbulence scatter. The measurementscarried out by Woodman and Guillen in 1971 used the Jicamarca radar operating at50 MHz, with 1 MW peak power, 5 km range resolution and the vertical pointingantenna with an aperture of 84000 m2. Because of the altitude coverage, these kindsof radar were later named mesosphere-stratosphere-troposphere [MST] radars.

The main parameters measured directly with an MST radar are the intensity orpower, the Doppler spectrum shift and the Doppler spectrum width of the radarechoes. Figure 3 shows a typical examples of a height-time contour plots of echoesfrom the mesosphere measured with the MU radar in Japan [Sato et al., 1985].Such observations at other MST radars show very similar features. The echostructures are observed in thin laminae [at 70 km] and short-lived blobs [at 07:00around 75 km] as well as in thick layers [long lasting structures around 70-75 kmin Figure 2]. Thin and persistent laminae are displayed in Figure 4 [an example ofVHF radar observations at low latitudes at the Arecibo Observatory on PuertoRico], are often characterised by a narrow spectrum width, i.e. small turbulentvelocity fluctuations, whereas the thick and intense layers can have a wide spec-trum resulting from large turbulent velocity fluctuations. The short and

Figure 4. Height-time intensity plots of mesospheric radar echoes measured at 46.8 MHz atlow latitudes at Arecibo, Puerto Rico.

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Figure 5. Radar echo power contours measured with the SOUSY-VHF-Radar (53.5 MHz)showing the tropopause and a tropopause break during a frontal passage (contour linedifference is 2 dB). The shading shows regions of high echo power. The circled cross hairsshow the tropopause, measured with radio sonde.

localised power bursts above 80 km in Figures 3 and 4 are not due to "turbulencescatter" but are due to meteor echoes. The mesosphere turbulence echoes occuronly during daylight hours or strong particle precipitation in polar regions, whensufficient ionisation is existent in the mesosphere. Other extra-ordinary echoes areobserved in the high latitude summer mesopause region, which are the polar meso-sphere summer echoes [section 7].

Figure 5 shows a height-time contour plot of VHF radar echoes from the lowerstratosphere and the troposphere, measured with the 53.5 MHz Sousy VHF radar inGermany [Röttger and Larsen, 1990]. These echoes are regularly observed withvertically pointing radar beam up to the lower or middle stratosphere, depending onradar sensitivity. Echoes from the lower troposphere are usually strongest, althoughthe echoes at higher tropospheric altitudes or above the tropopause [circles in Figure5] can also be enhanced due to increased turbulence or larger stability. The latter isfrequently observed to occur above the tropopause. We note that these observationsallow the detection of the tropopause and frontal passages [Gage, 1990; Röttger andLarsen, 1990].

For pure turbulence scattering, the echo intensity of the layers, laminae and blobsis a measure of the intensity of turbulence. For partial reflection, the echo intensity isa measure of the steepness and magnitude of the refractive index gradient. Hocking[1985, 1997] has reviewed the radar scatter mechanisms of these small scalestructures in the mesosphere and lower thermosphere. Regardless of the irregularitiescausing these MST radar echoes, the Doppler shift of the echoes is in a first approach

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proportional to the bulk radial velocity of the backscatter or reflection region. Thisfeature is commonly used to deduce the three-dimensional velocity vector. TheDoppler power spectrum width can, with certain precautions, be a fair estimate of theturbulent velocity fluctuations. The temporal variation of intensity is a measure ofthe persistency of turbulence or the stability of the gradient of refractive index. Bymeans of measuring the intensity at different antenna beam directions, the anisotropyof turbulence and gradient structures is investigated. By combining measurements ofvelocity fluctuations at different beam directions, the covariance of horizontal andvertical velocities, namely the Reynold stress due to atmospheric waves, is determin-ed [Vincent and Reid, 1983]. Using three or more horizontally spaced antennas, thehorizontal velocity vector and the horizontal coherence are deduced. This spaced an-tenna technique is also used in the interferometer mode which allows to investigatethe fine structure of turbulence and gradients [Röttger and Ierkic, 1985].

The outlined quantities are typically measurable with altitude resolutions of 150 mto about 1 km between about 60 km and 90 km in the mesosphere and up to about30 km in the stratosphere, depending on radar sensitivity and atmospheric con-ditions. The time resolution is adapted to the physical phenomenon of interest andcan be as good as a fraction of a second. Of particular interest is the turbulenceoccurrence and its intensity. These are linked to the turbulence energy dissipationrate. This in turn determines the structure constants of irregularities in the electrondensity, which in total constitute the turbulence refractive index structure constantCn2. This quantity can be deduced under certain conditions from radar echo powermeasurements, which then yield the turbulence energy dissipation rate. The dissi-pation rate can also be determined from the Doppler spectrum width, if instrumentaleffects are negligible or removed. All approaches need the knowledge of backgroundprofiles of temperature and electron density.

3.3. A Short View on the Transition from Turbulence Scatter[MST] to Incoherent Scatter [IS]

The main features of IS radar and MST radar scattering processes have beenbasically discussed in the previous chapters. In the mesosphere these processes areinterlaced, and one has to attempt to separate these. Essential criteria, characterizingthese two different processes, are the scattered power [scatter cross section] and theshape of the Doppler spectra of these radar echoes. For both cases the monostaticbackscatter results from variations of the refractive index at scales of half the radarwavelength, called the "Bragg wavelength".

Scatter of electro-magnetic waves results from fluctuations in the refractive indexin the scattering medium. The following discussions are based on the primary originof these fluctuations in the neutral atmosphere caused by turbulence. Thesefluctuations are usually described by the Kolmogoroff spectrum, which is sketched in

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Figure 6. The spectral density E(k) of these fluctuations is a function of the spatialwavenumber k. The spectral density is largest at small wavenumbers, i.e. at largespatial perturbation scales. It decreases with spatial wavenumber, i.e. the pertur-bations are getting weaker with shorter spatial scales. A detailed discussion of theseuniversal spectral forms was given for MST radar techniques by Hocking [1985]. TheKolmogorov spectrum is basically partitioned into several subranges: the buoyancysubrange, the inertial-convective subrange and the viscous-diffusive subrange. Thesesubdivisions had to be introduced when not only turbulent diffusion has to beconsidered but also diffusion of other additives, such as electrons and heavy ions inthe mesosphere. These are discussed for the particular phenomena of polar meso-sphere summer echoes by Cho and Kelley [1993], for instance, but will not be treatedhere. In the inertial-convective subrange the spectral density is E(k) ∝ ε 2/3 k -5/3,where the large turbulence eddies decay into smaller eddies. This is followed by

Figure 6. Simplified Kolmogoroff spectrum, showing the spectral density E(k) of atmosphericfluctuations as function of spatial wavenumber k = 2π/x, with x spatial coordinate. Whereasthe continuous line indicates the spectral density of neutral fluctuations, which are in a one-to-one correspondence with fluctuations of the ionized atmosphere (mesosphere, D-region),the dashed line shows the extension into a viscous-convective subrange in the electron gas re-sulting from fluctuations of electrons in the presence of heavy ions in the mesosphere (afterCho and Kelley, 1993).

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the viscous-diffusive subrange, where turbulence is dissipated into heat. Thefluctuation spectral density is E(k) ∝ (ε /ν 2)2 k-7, where ε is the turbulence energydissipation rate and ν the kinematic viscosity. A steep fall-off of the fluctuationsin the viscous-diffusive subrange is noticed. Finally, at sufficiently small spatialscales, the turbulence induced fluctuations will no more exist and only thermalmotions of the molecules will remain. When part of these molecules, which are inthermal equilibrium, are ionised [i.e. in the mesosphere], the refractive indexchanges are due to the random thermal motions of the charged particles in theionospheric plasma, namely the electrons in the presence of the ions. This Figure6 also indicates the scales of turbulent and thermal motions at which "coherent"MST radar scatter and "incoherent" scatter dominates, respectively.

The original "turbulence scatter" theory of MST radars bases on scatter fromisotropic turbulence at scales in the inertial-convective subrange of the Kolmogoroffspectrum. Beyond the viscous-diffusive subrange incoherent scatter from the freeelectrons occurs. There is consequently a transition from "turbulence scatter" in theinertial-convective subrange via the viscous-diffusive subrange to "incoherentscatter" at spatial wavenumbers beyond the high limit of the viscous-diffusive sub-range, where the process is in thermal equilibrium. The former scatter is called"coherent scatter", or "MST scatter". The latter is commonly called "incoherentscatter", but also the terms Thomson scatter or thermal scatter are used. It has to benoted that this transition region depends on the radar wavelength, the height andturbulence intensity. For the radars in question, operating between 50 MHz and 500MHz, this range is in the mesosphere.

The subranges of the Kolmogorov spectrum are limited at the outer and innerscales of turbulence, which in turn are dependent on the turbulence energydissipation rate, the buoyancy frequency and the kinematic viscosity. Theseparameters change with function of altitude. Hocking [1985] has calculated thesefor reasonable atmospheric models. In Figure 7 these range limits are shown asfunction of height and spatial wavenumber.

The turbulent velocity fluctuations in the inertial subrange cause the backscat-tered radar signal to be widened. The width of the measured Doppler spectrum of aradar at wavelength λ is given by [Hocking, 1985]:

ωt =

32 < w2 >

λ 2

½(1)

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Figure 7. Viscous, inertial and buoyancy subranges as function of altitude and spatial scale.The vertical line at the scale of 3 m shows the Bragg wavelength for monostatic 50 MHzradars (Hocking, 1985).

Figure 8. Half-power width (in logarithmic units) of power spectra of incoherent scatterechoes from the mesosphere and lower thermosphere for the frequencies 224 MHz and 931MHz of the EISCAT radars. f is the Doppler frequency and z is the altitude. fipp = c/2z(c = speed of light) is the minimum pulse repetition frequency, which can be used in pulse-to-pulse modulation.

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Figure 9. (a: left) Power spectra of incoherent scatter echoes from the mesosphere measuredwith the EISCAT VHF (224 MHz) radar and fitted theoretical spectra. (b: right) Amplitudespectra of polar mesosphere summer echoes measured with the EISCAT VHF (224 MHz)radar for turbulent (2 July 1987) and quiet (9 July 1987) conditions.

This assumes that all other effects, such as beam and shear broadening forinstance, can be neglected or are eliminated from the measured data. The root meansquared turbulent velocity fluctuations < w2 > are in turn related to the turbulenceenergy dissipation rate ε.

Thermal fluctuation cause the Doppler spectrum of the IS radar signal to bewidened. In the collision-dominated regime [mesosphere] of the Thomson scatterprocess, the variation of the spectrum width, of course naturally proportional to thesquare of the radar frequency, is primarily determined by ionospheric parameters[Mathews, 1985] and can be expressed in simplified form:

ωs ∝ Ti

νin .

mi + mn

mi mn . ( 1 + Λ- ) (2)

with Ti the temperature of the ions [assumed equal to the temperature of the

neutrals in the mesosphere], νin the collision frequency of ions and neutrals, mi

the mean mass of the positive ions and mn the mean mass of the neutral

molecules. The term Λ- is the ratio of the number density ni- of negative ions andthe number density ne of free electrons, which is usually called the electrondensity.

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It is obvious from Eq. 2 that this spectrum of incoherent scatter echoes widenswith increased Λ- and gets narrowed with the collision frequency νin. The reason isthat collisions damp the plasma waves which create refractive index variations. Thelatter, increasing exponentially with altitude, has the noticeable effect that theincoherent scatter spectra are getting narrower with decreasing altitude. Figure 8shows calculated incoherent scatter spectral width for the EISCAT radar fre-quencies 220 MHz and 931 MHz, deduced after Collis and Röttger [1990]. Even forstrong turbulence in the mesosphere, the spectral width resulting from turbulenceinduced electron density variations should usually be narrower than the spectralwidth of the incoherent scatter signal.

As long as the spectral width is smaller than the radar pulse repetition frequencyfipp, the so-called pulse-to-pulse technique can be applied. In other words, the signalcoherence time [the inverse of the spectrum width] in the pulse-to-pulse case islonger than the interpulse period, which is the inverse of the pulse repetitionfrequency. As Figure 8 shows, this condition holds for incoherent scattering fromaltitudes below about 85-90 km. Since the coherence time of turbulence scatter andreflection is much longer than the coherence time of incoherent scatter, the pulse-to-pulse technique is always applied in MST radar systems. This has the obviousadvantage in the application of coherent integration and complementary coding,including truncated codes [Ghebrebrhan and Crochet, 1992]. In the incoherentscatter case the multi-pulse, Barker coding or long-pulse technique has to beapplied above altitudes of 90 km. More detailed discussion of these techniques canbe found in Röttger [1989]; the alternating code technique is now replacing themulti-pulse technique [Wannberg, 1993].

Examples of measured incoherent scatter spectra are shown in Figure 9a formesospheric altitudes between 79 km and 96 km, which indicate the widening withincreasing altitude [compare with Figure 8]. In Figure 9b examples of spectra fromaltitudes around 85 km are displayed, which are much narrower than the incoherentscatter spectra [note: the indicated frequency span of 26.7 Hz in Figure 9b, ascompared to the 200 Hz span in Figure 9a]. These spectra in Figure 9b showsignatures of polar mesosphere summer echoes [PMSE, see section 7], which areagain different to incoherent or pure turbulence scatter. However, the width of thesespectra of PMSE in Figure 9b is still determined essentially by turbulent fluctu-ations. These spectra can be as narrow as a few Hertz, which is an indication ofvery weak turbulence, and a different scattering process. Röttger et al. [1990] havedescribed these spectra in more detail.

Spectra of MST radar echoes from the stratosphere and the troposphere are usual-ly even narrower than the spectra shown in Figure 9b, since the turbulence intensityis usually weaker in these lower altitudes and the scatter could be replaced oraffected by partial reflections.

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As Figure 7 shows, that Bragg wavelengths of VHF radars operating at 50 MHzare in the viscous subrange above about 70 km altitude. This means that scatterfrom turbulence induced ionisation irregularities should be too weak to cause adetectable radar echo. Following this model, only below about 60 - 70 km suchechoes should occur, provided that sufficient electron density exists in this lowerpart of the ionosphere.

The scatter cross section for incoherent scatter is in a first approximation givenby the number of electrons in the radar scatter volume times the cross section of asingle electron 4π re2 [re is the classical electron radius]. Collis et al. [1992] havecalculated the expected ratio of turbulence induced and incoherent scatter power asfunction of altitude for the EISCAT 224 MHz radar [Figure 10]. Depending onturbulence intensity, these echoes could be equal in power in the altitude region upto about 70 km. Collis et al. [1992] have actually found events of turbulence in-duced scatter superimposed on incoherent scatter observed around 68 km altitudewith the EISCAT 224 MHz radar. This proves the superposition of incoherentscatter and turbulence scatter at these mesospheric altitudes.

Figure 10. Ratio of echo power for scatter from pure turbulence (Pc) and incoherent scatter(Pi), calculated for the EISCAT VHF (224 MHz) radar for weak and strong turbulence energydissipation rates ε (Collis et al., 1992).

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4. The Scattering and Reflection of MST Radar SignalsLet us now discuss in a somewhat more quantitative way the influence of

turbulence-induced irregularities in electron density, neutral air density andtemperature as well as humidity on the scatter and reflection process governingthe MST radar method. More details of these mechanisms are described by Gageand Balsley [1980], Hocking [1985], Gage [1990], Röttger and Larsen [1990].

The MST radar echoes are caused by scattering or reflection from irregularities ofthe atmospheric refractive index. As in all backscattering processes of electro-magnetic waves, the backscatter arises from the component of the spatial spectrumof the variation of the refractive index n, whose spatial scale is half the radar wave-length for monostatic backscatter radars. This scatter is therefore also called Braggscatter [Gossard and Strauch, 1983]. The refractive index variations in the atmo-sphere result from random irregularities generated by turbulence, or to steep gra-dients introduced by horizontal layering or structuring of the atmosphere. Therefractive index variations are directly related to variations of the atmospheric para-meters: humidity, temperature, pressure [corresponding to air density] and electrondensity. The refractive index for the troposphere, stratosphere and mesosphere[ionospheric D-region] at VHF and UHF is:

n = 1 + ( 77.6 pT + 3.75·105

eT2 )·10-6 - 40.3

ne

fo2 (3)

where e is the partial pressure of water vapor [humidity] in mb, p the atmosphericpressure in mb, T the absolute temperature in Kelvin, ne is the ionospheric electrondensity in m-3, and fo the radar operating frequency in Hz.

The wet term, proportional to humidity, is usually most important up to themiddle troposphere, whereas, in the upper troposphere and stratosphere, the dryterm, proportional to pressure and inversely proportional to the temperature. Forradars operating in the lower VHF band, the ionisation of the D-region [given by ne]determines the refractive index in the height region between about 60 km and 100km. Polarization [Faraday rotation] and absorption effects are mostly neglected forVHF and UHF signals in the entire height range of the troposphere, stratosphere andmesosphere, although these are made use of by the MF radars detecting partialreflection echoes from the lower ionosphere, as mentioned earlier. During stong D-region ionisation in high latitudes the Faraday rotation can be quite pronounced at50 MHz for antenna beam directions almost parallel to the Earth’s magnetic field. Atfrequencies larger than several ten MHz [e.g., at 50 MHz], the turbulence-inducedscatter term will get very weak in the upper mesosphere [because of viscous sub-range limitations] and the incoherent scatter term will usually dominate the signal.For scales in the inertial subrange, clear-air turbulence in the mesosphere can yieldperturbations in the ionisation [D-region irregularities] and correspondingly in the

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radio refractive index n. In the presence of highly hydrated ions [clusters], however,the fluctuations in the electron gas can extend to much smaller scales than theneutral turbulence, which also could cause an enhancement of the refractive indexperturbations [Cho and Kelley, 1993]. Note that these irregularities are not createdby plasma instabilities, - they are either induced by turbulence in the neutralatmosphere because of the dominating collisions between ions and neutralmolecules in this height region or are resulting from cluster ions which cause theelectron diffusion and recombination to be changed and cause PMSE [see Figure1b]. The D-region irregularities are in certain cases be replica of neutral air turbu-lence, when one can neglect these latter sources or creation mechanisms due tochemical, hydration and recombination effects etc. [for more detailed discussionssee Cho and Kelley, 1993; Röttger, 1994a; Cho and Röttger, 1997; or Klostermeyer,1997].

When atmospheric turbulence or other small scale perturbations in the electrongas in the mesosphere mixes the vertical profile of the refractive index and theassociated gradients, fluctuations of n result, which in turn cause scattering andreflection of radar waves. It is useful to define a refractive index structure constantCn2 which is related to the mean square fluctuations <dn2> of the refractive index by

Cn2 = a <dn2> Lo-2/3 (4)

where a is a constant [≅ 5] and Lo is the outer scale of turbulence in the inertialsubrange, which is proportional to the square root of turbulence energy dissipationrate ε and the -3/2 power of the buoyancy frequency ωB of the atmosphere.

The turbulence refractive index structure constant can be expressed as:

Cn2 = 0.7 ε2/3 M 2 ωB-2 F1/3 (5)

Here F is the filling factor, i.e. the relative portion of the scatter volume which isfilled with turbulence irregularities, and M the generalised potential refractiveindex gradient.

For the unionised atmosphere it is found for the troposphere, where the humiditye is not negligible [specific humidity q = e / 1.62 p]:

Mt = -79·106 pT2

1 + 15.5·103 qT ·

T ωB2

g - 7.8·103

(1 + 15.5·103 qT)

dqdz ; (6)

for the stratosphere [humidity e is neglected]:

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Ms = -79·106 pT2 ·

ωB2

g ; (7)

and for the mesosphere [dominated by electron density ne]:

Mm = re λ2

2π

ne

ωB2

g - dρ

ρ dz -

dne

dz (8)

It needs to be noted that in these equations the vertical gradients of humiditydq/dz, temperature dT/dz, density dρ/dz and electron density dne/dz representaverages over the volume of turbulence, and that during turbulence development,these gradients will change. These derivations have been presented by Hocking[1985], who pointed out the said limitations. Observational evidence for thesedependencies are given by the fact that the mesosphere VHF radar echoes in non-auroral latitudes only exist during daylight hours when there is sufficient ionisation.Noticeable evidence for this was presented by Rastogi et al. [1988] who describedan increase in MST VHF radar scatter from the mesosphere during sudden electrondensity enhancement observed by 430 MHz incoherent scatter radar at Areciboduring a solar flare. Czechowsky et al. [1989] describe the relation of mesospherewinter echoes in auroral latitudes [see Figure 1c] on the D-region electron densitydeduced by riometer measurements. Also Collis et al. [1992] have detected on 224MHz a turbulence echo in the mesosphere during enhanced electron density andturbulence intensity. In Figure 5 the VHF radar echo enhancements in the lowertroposphere are noticed, which result essentially from humidity gradients in thelower troposphere and stable temperature gradients above the tropopause and in thetropopause break.

The radar reflectivity η at the wavelength λ for pure and volume scattering fromisotropic turbulence in the inertial subrange is:

η = 0.4 Cn2 λ-1/3 (9)

These relations hold only for radar wavelengths which are larger than the innerscale of the inertial subrange of turbulence fluctuations. As pointed out earlier, thisinner scale depends on turbulence intensity and the kinematic viscosity. The latterincreases as a function of altitude [see Figure 7], which places a lower limit to radarwavelengths which can be used to detect echoes from the middle atmosphere. Forscatter from fluctuations in the viscous subrange, which result from fluctuations ofneutral turbulence in the mesosphere an appropriate formalism to determine η is notavailable yet, since the dependency on background gradients of electron density isnot quite solved so far.

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The mean received radar echo power Ps for volume scatter is given by the radarequation:

Ps = α2 AE Pt δr

4 π r2 · η (10)

where Pt is the transmitter power, AE the effective antenna area, r the distance to

the centre of the scattering volume, δ r is the range gate width [corresponding tothe radar pulse length], and η the radar reflectivity.

Since it is assumed that partial reflections from steep vertical gradients of therefractive index are also observed by vertically beaming VHF radars, the radarequation has to be extended for this condition. Then the power received by re-flection is:

Pr = α2 Pt AE2

4 λ2 r2 · |ρ2| (11)

where |ρ2| is the amplitude reflection coefficient.

Model for Scatter/Reflection Mechanisms of MST Radar Signals

(conceptual synopsis)

MechanismAngular

SpectrumCoherence

TimeReflectivity

Structure

BRAGGSCATTER

(a) isotropic(b) anisotropic

constantwide

shortshort

random turbulence(a) isotropic(b) anisotropic

FRESNELSCATTER

(a) stratified(b) spread

narrowwide

intermediateintermediate

multiple laminaein stable environment

(a) horizontally stratified(b) range, angle spread

FRESNEL (partial)REFLECTION(a) specular(b) diffuse

narrowvery narrow

longvery long

one dominating laminaein stable environment

(a) very smooth(b) corrugated (rough)

Table 3. Conceptual synopsis of models for scatter and reflection mechanisms of MST radarsignals and typical characteristics: angular spectrum (aspect sensitivity), coherence time andthe generating reflectivity structures.

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The conditions of pure isotropic, volume filling scatter from turbulence inducedfluctuations is usually not realistic, and it is also generally not possible todiscriminate between these different processes of scattering and partial reflectionwithout investigating particular features of the MST radar echoes, such as theiraspect sensitivity, temporal and spatial coherency and their spectral shape or theiramplitude distribution functions. Now these different qualifications are discussed.

4.1. Composition of Scattering and Reflection from the Meso-sphere, Stratosphere and Troposphere

There is no unified opinion noticeable yet which mechanism may be the mostrelevant to cause the echoes of MST radars from the mesosphere, stratosphere andthe troposphere. One only could distinguish so far between the major process ofscattering/reflection from refractive index irregularities due to temperature,humidity and electron density fluctuations on the one side and the other twoprocesses, namely scatter from hydro-meteors [rain drops] in the troposphere aswell as incoherent scatter from free electrons in the mesosphere, which cause theobserved radar echoes. The major echoing process dominating the MST radarmethods can be described by several mechanisms as is defined in Table 3.

Figure 11. Height profiles of echo power observed with the 46.5 MHz MU radar at differentzenith and azimuth angles. The echo power is highest in the zenith direction, proving thestrong aspect sensitivity of the scattering/reflecting regions in the troposphere and lowerstratosphere (Tsuda et al., 1986).

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Figure 12. Height-time intensity plot of tropospheric and lower stratospheric fine structureobserved with 150 m height resolution and vertical beam at 53.5 MHz. The mean backgroundprofile is subtracted to improve the display of the thin layers and persistent laminae (Hockingand Röttger, 1983).

In order to explain the relevant MST radar observations, the two different basicechoing mechanisms, scattering and reflection, have to be assumed. These, however,have to be adapted into quite diverse deviations from these two idealistic cases. Formonostatic radars, backscatter and reflection arises from the component of thespatial spectrum of the variation of the refractive index n, whose spatial scale alongthe axis of the radar beam is half the radar wavelength, i.e. a few meters for lowVHF and less than a meter at UHF. This process is frequently called turbulencescatter, if a radar volume is homogeneously filled with randomly distributed, andisotropic irregularities; whereas it is called [partial] reflection if inhomogeneities inform of stable discontinuities or steps of the refractive index exist. The latter casemore likely applies to longer radar wavelengths. It is known that these two idealisedcases rarely occur but have to be replaced by more realistic models.

Since it can be assumed from the aspect sensitivity [Figure 11] and persistency[Figure 12] of radar echoes that partial reflections from steep vertical gradients ofthe refractive index [discontinuities] are observed by vertically beaming radarsoperating around 50 MHz, the radar equation for this condition was introduced. Theamplitude reflection coefficient, however, cannot be uniquely determined, since itstrongly depends on the shape of the refractive index profile within a distance ofless than one radar wavelength [Röttger and Liu, 1978; Woodman and Chu, 1989].

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Figure 13. Schematics of small-scale vertical variations of the refractive index showing thethree main processes Bragg scatter, Fresnel scatter and Fresnel reflection, accepted to be thecause of the MST radar echoes in the troposphere and stratosphere; _z is a typical range gatewidth.

It is also frequently observed that there is more than one partially reflecting re-fractive index structure in the radar volume. Recent high resolution in-situtemperature measurements [Luce et al., 1995] support this assumption of partialreflection from thin sheets or laminae [Figure 12], at least for the stratosphere.

It is not readily possible to discriminate between the different basic processes ofscattering and partial reflection, detected by MST radar, but in general it has becomeaccustomed in the MST radar community to apply a nomenclature which is basingon the principal schematics of the different refractive index formations shown inFigure 13 [Röttger and Larsen, 1990], and summarised also in Table 3. There existmany papers dealing with the theory as well as experimental methods to investigatethe scattering and reflection mechanisms and only the basic characteristics will bedelineated.

As defined in Table 3, the principle scattering mechanism in MST radar applica-tions is frequently also called "Bragg scatter" [Gossard and Strauch, 1983], ratherthan turbulence scatter. This term results from the physical mechanism ofconstructive interference of backscatter from spatial spectrum components at theBragg wavenumber k = 4π/λ of refractive index fluctuations in a turbulence layer,which is much wider than many radar wavelengths λ. The Bragg scatter can be iso-tropic, i.e. without causing a radar aspect sensitivity, if the turbulent irregularities ofrefractive index are homogeneously random and statistically similar in all directions.Bragg scatter can also be anisotropic, causing an aspect sensitivity if the statistical

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properties of the irregularities, namely their correlation distances, are dependent ondirection. Although the angular [spatial] dependence of the radar echoes, i.e. theaspect sensitivity, for these two processes - isotropic and anisotropic Bragg scatter -is different, the temporal variations of the radar echoes should be similar because ofthe randomly fluctuating irregularities. The Doppler spectrum should approximatelyreveal a Gaussian shape.

"Fresnel scatter" [Gage et al., 1981; Hocking and Röttger, 1983] occurs if,instead of a random ensemble of irregularities, just a few refractive indexdiscontinuities in vertical direction exist in the range gate. These discontinuities arestill randomly distributed in the vertical, but have a large extent, i.e. a longcorrelation distance in the horizontal direction. The radar echo characteristicsresemble a distinct aspect sensitivity, but because the discontinuities are statisticallyindependent, the temporal echo characteristics should be similar to those of Braggscatter. Because of the statistical distribution of the discontinuities, the averagepower profile should fairly smoothly vary with altitude. The term Fresnel scatter isused because the discontinuities should have a horizontal extent which is at least inthe order of a Fresnel zone.

"Fresnel reflection" [Röttger and Larsen, 1990] is observed if a single, dominat-ing discontinuity of the refractive index exists in vertical direction, which has alarge horizontal extent, similar to the ensemble of discontinuities for the case of

Figure 14. Amplitude spectrum of a 53.5 MHz radar echo from the troposphere measuredwith vertically pointing antenna and 150 m height resolution over eight minute post-integration time, showing spikes due to Fresnel scatter/reflection and a Gaussian-shapedbackground due to Bragg (turbulence) scatter.

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Fresnel scattering. A very distinct aspect sensitivity should be observed. Highresolution vertical power profiles or height-time intensity plots should reveal out-standing spikes, or thin and persistent structures, respectively. Also the temporalcharacteristics should indicate long coherence times. This kind of process is alsocalled "partial reflection", because only a very small fraction of the incident poweris reflected. Fresnel reflection is also called "specular reflection" by some authorsif the horizontal surface of the discontinuity is assumed to be very smooth, and itis called "diffuse reflection" if the discontinuity is assumed to be corrugated orsomewhat rough.

Fresnel scatter and reflection occur more likely on longer radar wavelengths, i.e.in the low VHF band. The terms Fresnel scatter and Fresnel reflection have beenintroduced due to the condition that the horizontal correlation distance of thediscontinuities is in the order of the Fresnel zone [r⋅λ]1/2, where r is the distancebetween the radar and the scatter/reflection volume, and λ is the radar wavelength.For correlation distances smaller than a fraction of the Fresnel zone, anisotropic orisotropic Bragg scatter can dominate. The Fresnel zones of radars in the UHF andVHF band are usually smaller than the region in the troposphere and stratosphere,which is illuminated by the radar beam. Thus, the beam width limiting effect has notto be considered. It is perceived that the definition of Fresnel scatter and Fresnelreflection depends on the range gate width, i.e., it is more likely to observe Fresnelscatter with coarse height resolution, and to observe Fresnel reflection with goodheight resolution. The discontinuities must be in the order of a radar wavelength, orless in vertical direction, but widely extended in horizontal direction, which,because of diffusion reasons, is more likely to happen at larger vertical scales. Thenomenclature of thin "sheets" or "laminae" to describe the 50 MHz observations[Röttger, 1980] was introduced and taken from oceanography where a similar finestructure is observed. The reason for the coexistence of refractive index turbulenceand discrete discontinuities [sheets or laminae] in the atmosphere could be for in-stance due to the gradients developing at boundaries of turbulence layers, or someother yet unproved mechanisms. For instance, Hocking et al. [1991] have suggestedthat viscosity waves and thermal-conduction waves can be a cause for the reflec-tions detected with MST radar. Simulations and computations, compared withdistribution functions of radar echoes on 50 MHz, demonstrate that signals do occurfrom certain altitudes which are consistent with the model of reflection from asingle, diffuse sheet, causing focussing and defocussing. The existence of sheets inthe temperature microstructure, which would be needed for Fresnel reflection orFresnel scattering, was proven by in-situ observations in the lower atmospherereported by Luce et al. [1995].

Although a fine structure of radar echo power is also observed on 430 MHz[Woodman, 1980a] and on 2380 MHz [Woodman, 1980b], it is not obvious that thefine structure observed on 50 MHz with vertical beam, is of similar origin or nature.

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It is likely that radars in the UHF band will only detect Bragg scatter from thinturbulence layers, whereas radars in the VHF band will usually detect a combinationof the different processes, particularly when using a vertical beam [Röttger and Liu,1978]. At 50 MHz there are usually weak Gaussian-shaped background spectraobserved on which narrow spikes are superimposed [Figure 14]. The Gaussian partsof the spectra are supposed to be partly due to Bragg scatter from a background ofturbulence, and partly due to scatter from off-vertical irregularities carried by thewind [beam width broadening]. The superimposed spikes in discrete frequency binsare either due to Fresnel scatter, or more likely due to Fresnel or diffuse reflectionfrom a rough surface, i.e. several discrete regions of high reflection coefficientwhich move with different velocities. It is noted that the spectra of 50 MHz radarsare not particularly governed by the spikes if the antenna is pointed far enough off-zenith [ >10o - 15o ], such that the isotropic Bragg scatter component dominates. It isalso noted from spectra, as well as from the aspect sensitivity, that Fresnel scatterand particularly Fresnel reflection yield generally a larger echo power than Braggscatter from turbulence.

5. Spaced Antenna and Interferometer TechniquesThe traditional method applied with MST radars to measure wind velocities is the

so-called Doppler-Beam-Swing [DBS] technique. More frequently also the so-calledspaced antenna mode [Briggs, 1984] has been adopted to deduce the wind velocityfrom the cross correlation analysis of signals received at separate antennas. This isthe so-called spaced antenna [SA] technique. Both these methods of course allow themeasurement of some additional parameters, such as the signal power, the cohe-rence time, the angular dependence or the spatial coherence as well as the amplitudedistribution functions. These are useful parameters to study the scattering/reflectionmechanism. Neither the Doppler nor the original spaced antenna method [whichdates back several decades, see references in Briggs, 1984] need the measurementof the spatial distribution of the signal phases on the ground. Several advantagesexist when amplitude and phase [i.e., the complex amplitude] measurements with aspaced antenna set-up are done [Röttger and Ierkic, 1985]. The applicability of thisradar interferometer method to deduce additional signal parameters, which the con-ventional Doppler and spaced antenna methods cannot supply, has beenconvincingly confirmed during the recent years [van Baelen et al., 1990, 1991;Palmer et al., 1991]. The application of the interferometer mode has gained im-proved insight into the spatial structure of the scattering/reflecting irregularities andcan also replace electronic beam steering by digital off-line processing [Röttger andIerkic, 1985; Kudeki and Woodman, 1990].

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Table 4. Advanced methods to analyze MST radar signals detected with spaced antennaarrays of UHF, VHF and MF radar systems: A = modulus of complex amplitude, ACF =auto-correlation function, CCF = cross-correlation function, CACF, CCCF = complexauto/cross-correlation function, CCFFT = complex cross fast Fourier transform, CFFT =complex Fourier transform, OSA = oblique spaced antenna method, FCA = full correlationanalysis, FSA = full spectrum analysis, SAV = spaced antenna velocity deduction, RI = radarinterferometry, IDI = imaging Doppler interferometry, PBS = post-beam steering, PSS =post-statistics-beam steering. These methods are applied to investigate the structure anddynamics of the troposphere, stratosphere and mesosphere with MST radars.

In accordance to the term frequency domain interferometry, the method usingseveral antennas is called the spatial domain interferometry or simply spatial in-terferometry. The spatial domain interferometry improves the resolution in thedirection perpendicular to the beam direction [i.e., mostly horizontal], whereas thefrequency domain interferometry [e.g., Kudeki and Stitt, 1987; Palmer et al., 1990]allows to improve the resolution in the radial [i.e, range] direction. The formermethod allows for instance to measure the angular spectrum [i.e., the aspect sensiti-vity], the incidence angle, the corrected vertical and horizontal velocity as well as todetermine horizontal phase velocities and the momentum deposition of atmosphericgravity waves and to track turbulence blobs. Post-beam-steering and the crossspectra analysis can be applied to study waves and turbulence in the stratosphereand the mesosphere, respectively. The original method of cross spectrum and cohe-rence analysis was developed to study scattering from E-region irregularities withthe 50-MHz Jicamarca VHF radar. This method was also applied to measure inci-dence angles with the Chung-Li VHF radar and to investigate polar mesospheresummer echoes with the 224-MHz EISCAT VHF radar. One envisages essentially

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more details of the scattering/reflection mechanism by the application of the spatialand frequency domain interferometry.

In Table 4 the different methods have been summarised, which can be appliedwith MST radar in the spaced antenna mode to measure atmospheric parameters.This is particularly emphasised since it is often thought that the spaced antennamethod is barely the spaced antenna drift technique to measure the drift speed ofrefractive index irregularities and deduce the horizontal wind. This technique is onlya minor part of the total, indicated by the branch including the square-law detectorin Table 4. All further applications make use of the phase information, such as theinterferometer, the post-beam-steering and the post-statistics method used with theSOUSY-, the Chung-Li and the Jicamarca VHF radar, respectively.

Also the oblique spaced antenna method has been applied [Liu et al., 1991], andradar imaging using a set-up of spaced antenna modules has been done for studyingthe irregularity structure [Kudeki and Surucu, 1991; Huang et al., 1995].

Figure 15. Profiles of spectra of echoes from the troposphere and lower stratospheremeasured on 7 Feb. 1992, 08:11 UT, with the EISCAT UHF radar.

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6. Example of Stratosphere-Troposphere Observationswith EISCAT

MST radars are usually operated in the Doppler mode, where several antennabeam directions are used to deduce the three-dimensional wind velocities from theDoppler power spectrum. Figure 15 shows an example of tropospheric scattermeasured with the EISCAT UHF radar [Röttger, 1994b]. Low elevation antennabeam directions had to be used in this stratosphere-troposphere mode due totransmit-receive recovery effects. A range resolution of 750 m was chosen,corresponding to a 250 m altitude extent of the scatter volume, when beaming at 20°elevation angle. The variation of the Doppler shift with height is a direct measure ofthe horizontal wind profile [shown in Figure 15 are the zonal and meridionalcomponents] and the width of the spectra is a coarse estimate of the turbulencestrength. It is obvious that at these low elevation angle and high frequency, theechoes are exclusively caused by turbulence scatter.

The on-line pre-processing is done by computations of the auto-correlation func-tion [ACF], which is the standard data preprocessing and compression methodapplied in EISCAT incoherent scatter experiments. The system hardware isoptimised for instrumental DC suppression. However, the kind of pre-processingdoes not include DC-elimination as usually done in MST radar applications. A smallamount of instrumental DC still remains and distorts weak atmospheric echoes atsmall Doppler shift. The ACFs are particularly contaminated by the DC component,which results from ground clutter from near-by high mountains. A special regressionalgorithm was developed to remove the DC contamination from the ACF. Thisneeds to be performed before the transformation into the frequency domain, whichusually is done for Doppler spectra analysis, since the truncation of the ACF wouldstrongly widen the DC component in the Doppler spectrum and spoil theatmospheric echo.

This algorithm, described by Röttger [1994b], turned out to be very efficient. InMST radar applications the removal of instrumental and ground clutter DC is usuallydone by high pass filtering of the real and imaginary part of the coherentlyintegrated raw data separately over a certain time interval which is long compared tovariations of the scatter signal. This filtering is done before any further off-linetreatment of the data. In the EISCAT system the complex autocorrelation function isfirst computed on-line. Depending on time scales to be investigated the auto-correlation functions are integrated over as much as several seconds or tens of se-conds. This has the advantage of extreme data compression, which is necessary inionospheric applications. This, however, seemed to have a disadvantage forstratosphere-troposphere applications in the presence of a strong DC component dueto ground clutter.

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Figure 16. Seasonal variation of MST radar echoes measured with the 49.9 MHz Poker Flatradar in Alaska, showing the increase in mesospheric echo power and of the altitude of theechoes during the summer months June and July (Ecklund and Balsley, 1981). These summerechoes were later named Polar Mesosphere Summer Echoes - PMSE.

7. Particularities of Polar Mesosphere Summer EchoesDuring the early operation of the Poker Flat MST radar in Alaska unusual meso-

spheric echoes were observed during the summer time [Balsley et al., 1980], asshown in Figure 16. After a long period of scepticism, whether or not these echoescould be created by enhanced neutral turbulence, several more reasonableexplanations were suggested, which base on fact that the polar mesopause is verycold in summer [Cho and Kelley, 1993].

These polar mesosphere summer echoes [PMSE] have now been observed overfrequency ranges of about three orders of magnitude between 2.7 MHz and 1.3 GHz.Echoes of similar characteristics were also observed in mid latitudes [Thomas et al.,1992] as early as the Poker Flat observations, and therefore the term mesospheresummer echoes is also used. A summary of the history of the PMSE observations isfound in [Röttger, 1994a], of which the part dealing with the scattering properties ofirregularities is repeated here.

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The scattering mechanism is basically the same on all these frequencies, namelyrefractive index irregularities have to exist at spatial scales of half the radar wave-length, i.e., between about 50 m and 10 cm. It is regarded as very unlikely that thesame properties of irregularities can cause the scattering over these wide ranges. Thepolar mesosphere summer echoes comprise a nice example of the transition from"coherent" to "incoherent" scatter, when applying radars in a wide frequency rangecovering the buoyancy subrange to the outer limits of the viscous-diffusive subrange[Figure 6]. An example proving the coexistence of incoherent scatter and theparticular scatter causing the PMSE is shown in the results of EISCAT observationson 931 MHz [Figure 17]. The weak and noisy incoherent scatter spectra noticed inall the range gates are dominated by very strong echoes with narrower spectralwidth in the range gates 84.7 km [Röttger et al., 1990], which are attributed to thePMSE scatter.

The EISCAT VHF [224 MHz] and UHF [931 MHz] radars have been used fre-quently in the recent years to investigate the polar mesosphere summer echoes.Almost all of the experiments were carried out in a single channel mode, i.e., onlyone antenna had been used for transmitting and for receiving. In those observationsonly the basic parameters, echo power, radial velocity and spectral width have beenobtained. Attempts using two collinear antenna sections of the EISCAT VHF systemin the interferometer mode were done by La Hoz et al. [1989]. As more and morenovel features of PMSE have been reported and are still far from completely under-stood [Cho and Kelley, 1993; Cho and Röttger, 1997], it became obvious that moreextended information on the irregular structure causing the PMSE is needed.Klostermeyer [1997] has developed a theory to explain PMSE scatter, which appearschallenging. Higher spatial resolution would be required to resolve apparent finestructure of the irregularities. More progress has now been achieved by applying theradar interferometer technique as introduced to the VHF radars for studying thelower and middle atmosphere by Röttger and Ierkic [1985] and successfully appliedwith EISCAT by Pan and Röttger [1996].

The frequency domain intereferometer method had also been introducedsuccessfully to study at PMSE with EISCAT [Franke at al., 1992]. With the spatialinterferometer method cross spectra of signals received at separated/spaced antennaspointing into the same direction, overlapping with the transmitting antenna had beendetermined. From these cross spectra, the coherence and the phase as function ofDoppler frequency are deduced. The height-time-intensity [HTI] plot of PMSE isshown in the upper panel of Figure 18a, which is reproduced from Pan and Röttger[1996]. The intensity [echo power] is displayed, where 45 dB corresponds to thenoise level. Thus, the signal-to-noise ratio was in the order of 20 dB. From this HTIplot a clearly layered structure is evident in the first 15 minutes of the observations.Two spectacular events occurred consecutively after the initial period of a persistent

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Figure 17. Power spectra of weak mesospheric incoherent scatter echoes and strong polarmesosphere summer echoes measured with the EISCAT UHF (931 MHz) radar at 00:33:00-00:33:40 UT and 00:37:00-00:17:40 UT on 2 July 1988. Each individual spectrum is anaverage over 10 sec and covers the frequency range ± 205 Hz. The strong spike observed inthe range gate 84.7 MHz is caused by PMSE.

and stratified structure of the layer. At about 09:38 UT the layer was liftedupward, followed by a downward motion and a billow structure then occurredsoon thereafter. This event is appearing as a cat’s eye structure that happened rightafter the originating up- and down-lift of the layer. The vertical displacement ofthe layer was about ±1.6 km. The disturbed layer became stratified again afterabout 09:55 UT. Such observations of cat's eye structures in mesospheric radarechoes were reported earlier [La Hoz et al., 1989] and are also seen as wavebreaking events in noctilucent clouds [Thomas, 1991]. These relate to intensityand velocity variations, which is expanded here into observations of spatial struc-ture of the irregularities causing the PMSE.

For a detailed structural study of this PMSE event the dynamic auto- and cross-spectra can be examined. The latter result from the signals detected at the two spa-tially separated receiving antennas, from which the coherence spectra [modulus ofthe normalised cross-spectra] are deduced. These are shown in the center [b] andlower panels [c] of Figure 18, respectively. These spectra result from a 64-point FFTspectrum performed per record of two seconds, and ten of these spectra arecoherently averaged to obtain the displayed auto- and coherence-spectra. Thecorresponding time step in this display is twenty seconds.

The high coherence values indicate that there exist deterministic individualscattering targets in the layer. It is assumed that these are patches of smaller irre-gularities which are frozen-in to deterministic spatial structures, which could resultfrom the different mechanisms as those suggested for instance by Havnes et al.[1992].

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Figure 18. (a) Height-time-intensity plot of PMSE observed with the EISCAT VHF radar (224MHz) on 16 June 1994. (b) Dynamic autospectra of the echoes in range gate 84.15 km. (c)Coherence spectra, deduced by the interferometer measurements of these echoes. Thecoherence limits are 0.3 to 0.7.

Due to the quite narrow spectral width, observed until the wave breaking, and therelatively high spatial coherence it occurs to us that the scattering structures are notgoverned by turbulence, rather than related to a stable environment. These pre-existing patches of irregularities, lined up in relatively narrow layer, are just affectedby wave motion. It is also argued that these pre-existing patches of fairly stableirregularity structures are just torn apart and blurred up by the turbulence event.

The feature of some distributed peaks found in certain Doppler cells of the coher-ence spectra in Figure 18c can be explained by the radar beam being filled withseveral detached structures. It is suggested that the PMSE is well organised duringthe initial observation period, and the wave breaking process just serves as a mech-

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anism of de-organising the PMSE irregularities. The observed effect, that anoriginally stable structure of scattering irregularities is only perturbed by neutralturbulence, was originally suggested by Röttger [1994a]. This can be supported byour observations of regions of high coherence, which are randomly distributedduring the time after 09:42 UT when the violent turbulence was observed. It is ar-gued that there is the same scattering mechanism responsible for the PMSE duringall our observations. It is also likely that those in-situ observations by Lübken et al.[1993], reporting wide layers of PMSE with strong velocity fluctuations and thinlayers with weak velocity fluctuations can be explained by these observations.

It has been shown that spatial interferometer measurements are essential to under-stand the intrinsic PMSE irregularity structure. It is not indisputable that differentscattering mechanisms are involved in these observations of PMSE, which showcalm as well as highly turbulent conditions. The appearance of layers and variationsin spectral width/fluctuations just displays the effect of the neutral atmosphere onpre-existing irregularities. These irregularities are, thus, effective tracers of theneutral atmosphere dynamics in the narrow range of observation.

8. Interpretations of Scattering and Reflection ProcessesThe interpretation of radar returns from the clear air of the middle and lower

atmosphere has been and still is in a long-lasting dispute. Is this just resulting from asemantic misunderstanding or preference of approaches to study the phenomenon ordoes it result from different physical phenomena? There are certainly differentmeteorological and aeronomical phenomena, which cause the different signalcharacteristics. In any case one can discriminate between the two extreme models ofthe echoing process itself:

[1] Scatter by random, non-deterministic fluctuations of the refractive index inspace and time, which can be isotropic and anisotropic. These fluctuationsresult from neutral air turbulence of convective or dynamic origin. Theanisotropic approach, however, is already at the limit of becoming deterministicin two coordinates.

[2] Reflection is from a refractive index discontinuity between horizontallystratified air masses of different refractive index, resulting from horizontal flowpattern, radiation, evaporation or electron density structures in the mesosphere.There are also clear indications for the coexistence of the two major mecha-

nisms, namely the thin and almost horizontally stratified laminae of refractiveindex, which appear to be corrugated by background turbulence, the pronouncedaspect sensitivity and long persistency which transits into isotropy and randomfluctuations at larger aspect angles and the non-Gaussian shape of the Dopplerspectra and signal components.

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It was suggested by Röttger [1994] that principally five different classes of meso-spheric irregularities occur, causing the polar mesosphere summer echoes atdifferent radar frequencies:

[1] Steep gradients of electron density,[2] electron density irregularities caused by mixing in gradients by neutral

turbulence,[3] extension of fluctuations in the electron density to shorter scales than in the

neutral density due to presence of heavy cluster ions [extended subranges asshown Figure 6 due to enhanced Schmidt number; Cho and Kelley, 1993],

[4] electrostatic waves due to of highly charged aerosols,[5] charge accumulation in electron clouds dressing multiply charged aerosols and

ice particles.The processes causing PMSE are interlaced and range from partial reflection

[around several MHz], turbulence scattering [around a few 10 MHz], scatteringrelated to enhanced Schmidt numbers or electrostatic waves [several 10 MHz toseveral 100 MHz] to enhanced Thomson [incoherent] scatter [around 1 GHz orhigher].

In Table 5 [from Röttger, 1994a], the different mesospheric phenomena aresummarised, which had been assumed to cause scattering of radar and radio waves.All the scattering/reflection mechanism of the electro-magnetic waves causing thePMSE require that refractive index irregularities exist at spatial scales of half theradar wavelength [for monostatic radar backscatter]. In Table 5 the scale relates tothe irregularity and the half radar wavelength scale. The assumed phenomena areordered according to the scales at which they can occur and cause scattering.Examples of PMSE of all the referenced radars were described by Röttger [1994a],and references can be found therein. Detailed descriptions of the status ofobservations and theories were published by Cho and Kelley [1993] and Cho andRöttger [1997]. Further theories related to the generation mechanisms of polarmesosphere summer echoes have recently been published [see review by Cho andRöttger [1997], and Klostermeyer [1997]].

The summary of the present knowledge indicates that the essential requirementsfor PMSE are cold mesopause temperatures, modulated by long-period waves andtides, and the D-region ionisation. Also needed are some contaminatingconstituents, e.g. aerosols or dust or ice particles [Cho and Kelley, 1993;Klostermeyer, 1997]. Neutral turbulence is playing a certain, but likely not thedominant role in the creation of the PMSE. However, the PMSE characteristics areundoubtedly also affected by short-period waves and turbulence. The most properconditions for these kind of mesosphere characteristics are found in the polarmesosphere in summer. It is not excluded, however, that similar conditions canoccasionally also occur at lower latitudes, which is supported by observations of

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strong mesosphere radar echoes in midlatitudes. Balsley et al. [1995] have reportedless frequent PMSE in the Antarctic, which they explain by higher mesopausetemperatures in the southern hemisphere polar atmosphere. It is recognised thatPMSE studies give a wealth of information on the aeronomy of the mesosphere.Also a multitude of dynamical effects, such as gravity wave propagation [Cze-chowsky et al., 1989], saturation and breaking into turbulence [Fritts et al., 1988],steepening and the possible occurrence of solitary waves can be studied [Röttger,1991]. It is to be assumed that these dynamical effects do not cause the PMSE, butthe PMSE act as sensors, in a similar way as noctilucent clouds [Thomas, 1991;Reid, 1995], which are to be associated with the polar mesospheric clouds and likelyPMSE, allow the study of mesospheric chemistry and dynamics.

Long-period waves can undergo non-linear steepening or tilting when their phasevelocity approaches the wind velocity. Through the approach of superadiabaticlapse rate and velocity shear, Kelvin-Helmholtz instability [KHI] is activated andquasi two-dimensional turbulence is generated. Turbulence scatter or Fresnelreflection from the boundaries of the turbulence layers can occur. Also steeptemperature inversions [stable sheets or laminae] could be caused by the steepenedwaves, which can be seen by Fresnel reflection.

Table 5. Mesospheric phenomena recognized as possible causes for polar mesospheresummer echoes.

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Short-period waves, propagating upwards from lower atmospheric sources orgenerated in-situ by KHI or by two-dimensional turbulence arising from long-periodwaves, undulate these layers of turbulence or the laminae of temperature inversions.Besides of transferring energy to long-period wave modes by wave-wave interactionthese short-period waves can grow in amplitude by KHI [local generation] or due toenergy conservation of upward propagating waves. Non-linear tilting, steepeningand/or parametric instability can occur. The development of tilting can be observedby Fresnel reflection due to the concurrent distortion of isotherms during KHI.

Non-linear tilting of short period waves can cause overturning and breakingthrough the Rayleigh-Taylor instability [RTI]. Since this happens at certain phasesof the wave, localised regions of small-scale turbulence occur. These are seen byVHF radars as blobs or bursts, which are propagating with the phase speed of thewave. Blobs can spread into wider spatial scales by multiple repetition of KHI/RTIand cause thick layers of strong turbulence. Through the turbulence layers corru-gated temperature gradients are generated and the layers can dissolve into multiplesheets or laminae which can be regarded as remnants of active turbulence. Againwaves, generated elsewhere, can undulate these turbulence layers and the laminae.Also viscosity waves and thermal-conduction waves have been suggested as a causeof partial reflection from the middle atmosphere [Hocking et al., 1991]. The recenttheory of Klostermeyer [1997] to explain the PMSE seems to offer a most attractiveexplanation.

There had been some interesting recent developments and approaches for improv-ing our understanding of the radar returns and the atmospheric structure, these are:The measurement of the frequency dependence of the MST radar echoes, the analy-sis of the signal statistics, modelling of the structures and the resulting radar returns,interferometer applications in space and frequency, and wind field measurements forinstance. Further understanding will be gained by the combination of radar measure-ments with other methods, such as in-situ measurements with balloons, rockets andaircrafts. Also the extension of radar systems by radio-acoustic-sounding systems[RASS] and LIDAR measurements is turning out to be very useful and should befollowed up in further coordinated campaign operations.

9. Future High-latitude Mesosphere Observations withRadar

The mesosphere can be studied with the incoherent scatter, as well as with theMST [mesosphere-stratosphere-troposphere], radar technique. Incoherent scattermeasurements of the lower thermosphere and mesosphere allow the derivation ofelectron density, ion-neutral collision frequency [neutral density] and temperature,ion [neutral] velocity, ion composition and the density of negative and positive ions,provided some assumptions can be applied. Occasionally coherent scatter from

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ionisation irregularities can mask the incoherent scatter measurements, particularlyin summer when Polar Mesosphere Summer Echoes occur.

EISCAT observations of the middle atmosphere and lower thermosphere hadbeen summarised by Röttger [1994c]. At the frequencies used by EISCAT inTromsø [224 MHz and 931 MHz], as well as at the EISCAT Svalbard Radar [ESR]operating frequency of 500 MHz, the turbulence scatter contribution to echoes frommesospheric altitudes is usually negligible. The reason is that the radar wavelengthon 500 MHz is much smaller than the scales of turbulence which can exist in themesosphere. To operate the 500 MHz as an MST radar to study mesosphericturbulence will therefore be impossible, unless a separate radar on a lower frequencysuch as 50 MHz would be set up. Simultaneous operation of a 50 MHz and a 500MHz radar would be a useful combination for mesospheric studies, however, sincethe former would be sensitive to mesospheric clear air turbulence and the latter toionospheric electron density. A 50 MHz radar would be also an optimum choice forstudies of the troposphere and lower stratosphere, since it detects echoes from clearair turbulence and inversion layers.

An appropriate complement to the 500 MHz incoherent scatter radar would be anMST radar [operated at frequencies in the 50 MHz band], which uses ionisationirregularities, related to neutral air turbulence and the effects of heavy ions, as scat-terers for studying the mesosphere. Compared to the incoherent scatter radar theMST radar has to be operated on relatively low frequencies, around 50 MHz, toobtain sufficient scatter cross sections. Usually the scatter cross section in MST scat-ter case is orders of magnitude larger than the scatter cross section in the incoherentscatter case. Consequently the transmitter power and antenna gain of an MST radaroperated on 50 MHz can be much smaller than that of the incoherent scatter radaroperated on 500 MHz. MST radars operate with beam directions close to the verticaland a mechanical antenna rotation to low elevation angles is therefore not neededfor this application. The MST radar measurements allow the deduction of the three-dimensional velocity profiles as well as turbulence intensity in the mesosphere,stratosphere and the troposphere.

Now observations of the mesosphere, stratosphere and the troposphere will bebriefly outlined, which can be made with an MST/ST radar operated in the polar orArctic atmosphere. The mesosphere observations are to be done in the incoherentscatter mode and/or the MST mode.

9.1. Coupling Processes between the Lower Thermosphereand the Mesosphere

Particular phenomena in the polar atmosphere and the auroral ionosphere, namelyparticle precipitation, Joule heating, electric fields and Lorentz forcing as well asvertical transport of constituents and momentum, which result from magnetosphere-

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ionosphere coupling, have an impact on the middle atmosphere. Furthermore dyna-mic processes, such as tides and gravity waves, which originate in the lower atmo-sphere [troposphere] and the middle atmosphere [stratosphere and mesosphere],propagate upwards into the thermosphere. These mutual coupling processes, whichaffect the structure, dynamics and aeronomy of the middle atmosphere and lowerthermosphere, take place uniquely in the high latitude mesosphere, where the effectsfrom the magnetosphere and ionosphere merge with the effects from the lower andmiddle atmosphere.

The EISCAT UHF and VHF radars have already demonstrated the ability to studycoupling processes from above to below in the lower thermosphere of the auroralzone. Several mesosphere/D-region investigations have been done with EISCAT,such as for instance the impact of precipitating electrons and protons on the D-region electron density and composition. How these coupling processes between themagnetosphere and the ionosphere, the thermosphere and the middle atmospheretake place in the polar region is so far unknown, since appropriate radar instrumentsare not operated at these high latitudes near 80°. For instance, the influx of solarprotons into the polar mesosphere and upper stratosphere evidently has an influenceon the ozone budget and can be studied by the Svalbard Radar. It would also be use-ful to allow simultaneous radar experiments in the auroral zone [EISCAT] and in theArctic [Svalbard] to study the meridional variation of these effects and how theirextension to lower altitudes in the middle atmosphere takes place.

Specifically, the EISCAT Svalbard Radar in the MST mode should be applied toobserve and study mesospheric temperature and winds, the possible auroralinfluences and the transport of nitric oxide as well as solar proton events [SPE] andthe resulting polar cap absorption phenomena [PCA] and their impact on middleatmosphere ozone and dynamics. The extent of Polar Mesosphere Summer Echoes[PMSE] and their relation to Polar Mesosphere Clouds [PMC] and NoctilucentClouds [NLC], Sudden Sodium and Sporadic-E layers needs to be studied in polarlatitudes. The winter anomaly of absorption and its relation to stratospheric warmingin the polar vortex is not known in the high latitudes of 80°. Most essential appearsalso the climatological study of winds, tides and long period waves and particularlythe climatology of atmospheric gravity waves [AGW] in the polar mesosphere, thesupposed acceleration of the mean wind by AGW momentum deposition and theeffect on the mesopause temperature.

For these obvious reasons the EISCAT Svalbard Radar should will have thecapability to make high standard observations of the D-region and the mesosphere,in addition to the planned studies of the ionosphere and thermosphere. An additionalMST radar, operated in the low VHF band near 50 MHz will be an invaluable tooland complement to the EISCAT Svalbard Radar for studies of the middle and loweratmosphere at very high latitudes.

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9.2. The Polar Stratosphere and Troposphere Investigated byST Radar

There are certain phenomena in the polar middle and lower atmosphere whichneed to be studied by radar, in addition to the multitude of other experiments whichare already applied for these studies in the Arctic and Antarctic, particularly thosedirected to the ozone problem. Only those phenomena will be discussed, which areassumed to be investigated with an ST radar [stratosphere-troposphere radar].These are the structure and dynamics of the troposphere and the lower stratospherein the polar region. The capabilities of ST radars for these studies are outlined in thereferenced review articles.

With ST radar wind profilers it is possible to study dynamic processes in a widescale range from planetary and synoptic scale disturbances to small-scale gravitywaves and clear air turbulence. The wind field variations occurring in the polarvortex can be monitored continuously by ST radar wind profiler, although only atone location and up to about 20-30 kilometers height. In polar regions it seems ofspecial interest to investigate with radar the exchange pro-cesses between the troposphere and the lower stratosphere, namely the variation ofthe tropopause height and the dynamics of tropopause foldings and fronts. Thepossibility to study vertical transport between the troposphere and the strato-sphere, and the transport within the stratosphere by means of the mean verticalmotion and by turbulent diffusion, is challenging. The transport and deposition ofenergy and momentum by gravity waves in the lower stratosphere, which can bemeasured with ST radar, is also believed to have an impact on the mean strato-spheric circulation and the polar stratosphere temperature. Furthermore, PolarStratospheric Clouds, which are assumed to be related to mountain waves, havecontrol of the ozone depletion. The formation of mountain waves can be studiedby ST radar and thus the dynamics in and around Polar Stratospheric Clouds canalso be investigated by the EISCAT Svalbard Radar in the ST mode. Such an STradar, if it would be operated continuously, would also yield invaluable input datafor meteorological modelling and forecasting. In summary, ST radar observationscan contribute considerably to the study of the structure and dynamics of the Arc-tic stratosphere, which is outlined in the sketch of Figure 19.

It is critical to understand the dynamics of the polar stratosphere before a com-plete picture of the ozone depletion phenomenon can be obtained. Expert scientistspropose that further acquisition and examination of a broad range of chemical aswell as dynamical observables will be necessary to address the challenging andimportant question of whether the processes leading to the Antarctic/Arctic ozonehole can also occur in other parts of the Earth’s atmosphere.

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Figure 19. A sketch of the structure and dynamics of the troposphere, stratosphere andmesosphere, as well as aeronomic and electrodynamic phenomena in the lower ionosphere,which can be observed by MST radar and incoherent scatter radar.

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10. Realization of an MST Radar on SvalbardNone of such ST radar observations outlined above have been done so far at the

high latitudes of 80° of Svalbard. In northern Scandinavia and Svalbard severalcampaigns were performed so far using different kinds of instruments, but STradar[s] were not employed on Svalbard. It is noted in several recent publicationson the ozone campaigns that investigations of Polar Stratospheric Clouds areimpossible without a rather significant initial investment in high-technologysensors such as satellites, mobile lidar systems and dedicated aircraft. TheEISCAT Svalbard Radar, together with an appropriate MST radar, could become amost appropriate and cost-efficient instrument to support these studies effectively.It is also worth repeating here that more then just one parameter can be measuredsimultaneously by ST radar, including the three-dimensional wind velocity, itssmall-scale divergence and the covariance of the velocity field, as well as theturbulence intensity and morphology and fine-scale and meso-scale structure ofthe troposphere and the lower stratosphere.

The present EISCAT UHF and VHF radars in Tromsø cannot be used for thepresented research tasks to study the troposphere and the stratosphere. Firstlybecause their location is not close to the polar cap, secondly that a frequency of 50MHz would be preferred; thirdly because ground clutter heavily masks almost allthe tropospheric and lower stratospheric ranges and the recovery and pulse repe-tition frequency are not sufficient; and finally because the EISCAT radars cannotbe operated continuously, which is deemed essential for most of the outlinedclimatological studies. Rather than upgrading and modifying the EISCAT radarsystems for this purpose, which might be quite expensive, one should aim to addMST capabilities to the EISCAT Svalbard Radar in an expansion phase and byadding a separate 50 MHz [M]ST radar system [Röttger and Tsuda, 1995].

11. SummaryThis article, consisting of a combination of several tutorials and reviews, is

supposed to be used as an introduction to radar research of the lower and middleatmosphere in high latitudes. Since there is an overlap or transition region ofincoherent and coherent scatter in the mesosphere, which particularly the EISCATradars can observe, it was tried to describe briefly the differences of thesescattering processes. In general, this article is aimed to summarise basics of atmo-spheric research using the MST radars, and possibilities are pointed out how thiscan be achieved in the high latitudes by combining the new 500 MHz EISCATSvalbard Radar with an MST radar to be established on Svalbard.

One regards combinations of radars operating at different frequencies as anessential tool to investigate these dynamical and aeronomical phenomena. Thecombination of radar observations with other instrumentation such as lidar and

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rockets as well as remote sensing from the ground and space will be needed tofully understand the dynamics, structure and aeronomy of the mesosphere, and thedynamics and structure of the stratosphere and troposphere.

Acknowledgements.

The author thanks the editor, Denis Alcaydé, for his encouragement to prepare this articleand for his patience to get it finished. He appreciates the numerous useful discussions withmany colleagues on the complex phenomenon of scattering and reflection from the middleatmosphere and the techniques applied to study these processes.

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